Per Chandler Rome of the Houston Chronicle, Astros manager A.J. Hinch announced Peacock's diagnosis Tuesday, and the right-hander is not with the team.
Noah Syndergaard of the New York Mets and J.A. Happ of the New York Yankees have had stints on the 10-day disabled list due to the virus.
Per the New York Department of Health, hand, foot and mouth disease causes a blister-like rash and has no specific treatment.
After coming up through the minors as a starter, Peacock has carved out an excellent niche in Houston's bullpen. The 30-year-old has a 2.98 ERA with 90 strikeouts and 46 hits allowed in 60.1 innings over 55 appearances in 2018.
Houston is tied with the New York Yankees at 90-54 for the second-best record in MLB. The defending World Series champions have a three-game lead over the Oakland Athletics in the American League West.