Ramirez is batting .283 and leads Boston with 15 home runs and 38 RBIs. He's missed the past four games after being hit by teammate Xander Bogaerts' line drive in last Wednesday's win over Baltimore.
Red Sox manager John Farrell said Ramirez would hit in the cage when he arrived in Toronto, where the Red Sox began a four-game series Monday.
''The optimistic view is that he'd be back in the lineup while we're here,'' Farrell said.
Second baseman Dustin Pedroia (right hamstring) is improving, Farrell said, and is expected to take batting practice during the series in Toronto.
Ryan Hanigan (broken right hand) is catching the first game and will DH the second game of a doubleheader at Double-A Portland on Monday. He's expected to come off the 60-day disabled list when he's eligible Wednesday.