While all fonts on Google Fonts are open source, the actual restrictions on their use depend on the specific open source license they're released under, which varies between fonts — there is no single license that would apply to all of Google Fonts.
The most common licenses on Google Fonts seem to be the SIL Open Font License and the Apache License 2.0. The former is a "copyleft" license designed specifically for fonts, and requiring any modified versions to be released under the same license, while the latter is a generic permissive open source software license that doesn't require modified versions to be released under the same license, but does require them to retain any applicable licensing, copyright, patent, trademark, and attribution notices from the original font.
In any case, if you actually read the text of those licenses, you'll note that even the SIL Open Font License only talks about "Font Software", and doesn't make any explicit reference to using the font in a logo or other visual artwork. The likely reason for this apparent omission is the curious copyright status of typefaces — to make a long and complex story short, in many countries (including the U.S.) the visual appearance of a font is not protected by copyright. Thus, the only copyright-eligible part of a modern computer vector font is the specific computer code in the font file that tells your computer how to render the (uncopyrightable) letter shapes on the screen in (what one would hope to be) the optimal manner.
What all this means is that, if you're only using the letter shapes from a font in your logo (and not the actual code from the font file), then you're probably allowed to do that regardless of how the font is licensed. Of course, there are a number of possible exceptions to that:
If you're designing the logo in a vector drawing program like Illustrator, and importing the vectorized letter shapes directly from the font, it's possible that the specific placement of the curves and control points used to draw the letter shapes may be considered "computer code" that is directly derived from the code in the font, and thus subject to the font's licensing requirements.
If this worries you, the standard work-around is to first render the letters as high-resolution bitmap images (which the U.S. Copyright Office, at least, has explicitly ruled to be ineligible for copyright) and then retrace them. The resulting vector shapes, while perhaps visually similar to the original font, cannot then be claimed to contain even the slightest possible trace of the original font code. (For those interested in this kind of thing, the landmark court decision about this in the U.S. is Adobe v. Southern.)
All this varies by jurisdiction. Not all countries consider typefaces to be ineligible for copyright, and if you and/or the font designer happen to live in a country that allows the visual appearance of fonts to be copyrighted (e.g. Russia), then your logo may have to abide by the font license.
This could be particularly problematic if the license assumes that the visual appearance is not copyrightable, and thus fails to explicitly grant any permission for using it in typesetting; for example, a strict (and, admittedly, untrained) reading of the SIL Open Font License would seem to suggest that, in jurisdictions like Russia, any document typeset with an OFL-licensed font would count as a derivative work, and would thus need to be released under the same license.
Some countries (e.g. the UK) may also consider typefaces to be copyrightable per se, but grant specific exemptions e.g. for "the ordinary course of typing, composing text, typesetting or printing." The question then becomes whether, and to what extent, using the font in a logotype falls under these legal exemptions. The only generally reliable recommendation I can give here is, in case of any doubt, to consult a local copyright lawyer.
Even in jurisdictions like the U.S., where the visual appearance of a font is not eligible for copyright protection, it may still be eligible for a design patent or some other similar legal protection. While it seems unlikely that someone designing an open source font would explicitly apply for a design patent on it, some jurisdictions (like, notably, the EU) automatically grant a short-term protection (e.g. 3 years) for all novel designs.
Finally, fonts can, of course, also be trademarked. Typically, a trademark on a font would only protect the name of the font, and thus would not matter when using the font e.g. in a logo. That said, in principle, I see no reason why a font could not contain a trademarked symbol (or part of one) as one of its characters, even if that seems an unlikely thing to do. In any case, there's nothing strictly specific to fonts here — regardless of how you design your logo, you need to ensure that the end result is distinctive from any competitors' trademarks.
OK, so what's the take-home message from all this? While I am not a lawyer, as a layman I would guess that:
you're probably fine, especially if you happen to live in a jurisdiction like the U.S. where the visual appearance of fonts is not copyrightable, but
if you have any doubts, the safe course is to either consult a local intellectual property lawyer, and/or just contact the font designer and request their permission to use the font (which you should obviously get in writing, and maybe show to a lawyer if you're not sure that it doesn't have any unexpected loopholes).
In the end, in practice, a lot will depend on just who you're designing the logo for. If it's for a small local business, you could probably get away with even quite blatant copyright infringement, simply because it's unlikely that anybody would bother to sue you even if they technically could. On the other hand, if you're designing a logo for a large multinational company (or, perhaps, for a startup aiming to maybe someday become one), you may want to be extra diligent just in case.