The Georgia Poison Center said both men, who had histories of psychiatric problems, are expected to recover, the Atlanta Journal Constitution reports.
Poison Center Director Gaylord Lopez told the AJC that living through a pandemic can be especially difficult for those with mental health issues.
Lopez said he could not release further details about the cases because of patient confidentiality concerns.
According to AJC, the Georgia Poison Center became aware of both cases after receiving calls from hospitals.
Trump has since backtracked his comments and said he was being sarcastic when he floated the idea that injecting disinfectants may be a way to treat coronavirus.