Martinez is batting .284 with 21 home runs and 68 RBIs in 104 games.
“He felt sick last night, has been feeling sick the whole day,” manager Alex Cora said.
Boston, which had lost seven of eight and fallen out of the AL East lead, put rookie outfielder Jarren Duran on the COVID-19-related injured list Friday. Neither Martinez nor Duran has tested positive, Cora said.
To replace Martinez, the Red Sox recalled catcher Connor Wong from Triple-A Worcester.
Right-hander Tanner Houck will be the 27th man for Saturday’s doubleheader against Toronto. Houck was expected to start Game 2 in place of left-hander Martín Pérez, who was moved to the bullpen Friday.