Can a person be held liable for copyright infringement for sharing a
meme on social media?
Yes, unless some other exception applies.
There is no specific exemption from copyright law for sharing a meme on social media.
Generally speaking, since sharing a meme on social media involves publishing the entire work to everyone in the world with Internet access, "fair use" is not a very strong defense to a copyright infringement claim in this context.
A more viable defense is the doctrine of "implied license" which is the idea that the original person to post a meme on the Internet did so with the implied intent that it be shared widely without a further grant of permission. For this reason, copyright disputes rarely arise from the sharing of a meme on social media.
But if the original person to post a meme on the Internet did so without permission of the owner of the copyright to the meme, it is an infringement of the copyright of the meme to share it on social media. This is true even if sharing the meme on social media is merely an innocent infringement made in the good faith belief that it was being shared with the permission of the copyright owner.
A claim of innocent infringement status for someone infringing a copyright by sharing a meme on social media is supported by Terms of Service for social media sites that turn over copyright to posted material to the social media provider (with an express right to share it on the site) in cases where the material is provided by the author of or owner of the meme for copyright purposes. Also, another Terms of Service states that users promise not to post copyright infringing materials on the site without permission to do so. Both of these terms of service provisions are ubiquitous on social media sites.
But, innocent infringers are still subject to lawsuits for money damages for copyright infringement, just not with all of the same remedies as in cases of intentional copyright infringement.
Social media sites themselves are immune from copyright infringement liability under Section 230 of the Digital Millennium Copyright Act (DMCA) under U.S. law (where most social media firms are based), however, so long as they comply with takedown notices in the manner provided by the DMCA. Usually, if a copyright infringing meme is taken down by a social media site, the copyright owner will not pursue other users of the site who innocently infringed their copyright by sharing a meme posted by someone else, although the law does not require them to do so.
What is international law on it?
Copyright law primarily arises under the domestic laws of a country. There are some treaties such as the Berne Convention that seek to standardize copyright law internationally, which many, but not all countries, have adopted.
But, in every case, analysis of the specific instance of sharing a meme on social media is not specifically addressed by international treaties, in part, because the practice did not exist when the vast majority of these treaties were entered into by the countries that are parties to them.
Facebook, for example, didn't come into existence until October 28, 2003, and the widespread practice of sharing memes on social media is more recent than that.