Price threw just 15 pitches. He retired the first two batters before giving up a single, after which manager Alex Cora came to the mound for a discussion, and Price left the game.
It was his second start after returning from a stint on the injured list with elbow tendinitis, though Cora reaffirmed during an interview on Fox's game broadcast that Price's early exit was not due to any arm injury.
"It's not his arm. He's been battling the flu for four days and his progression throughout the week wasn't the right one," Cora said. "We were proactive."
Price said after the game, a 4-3 Boston loss, that he wanted to keep pitching when Cora came out to visit the mound.
"I could have just ducked this start from the get-go. I didn't want do that; I didn't want to put is in that position," Price said. "I went out out there are tried to take the ball and AC didn't like what he saw so he took me out of the game. I wanted to stay in the game.
Cora said Price was "too valuable" to risk a further setback, saying the pitcher had been ill since before his first start following his return from the IL.
"He's been battling since the start in Toronto. It wasn't a normal week for him. I talked to him before the game and said, 'We don't need heroes here.'
"When he came in after he warmed up, [Red Sox catcher] Sandy [Leon] talked to me a little bit. [Pitching coach] Dana [LeVangie] talked to me a little bit. I saw him and talked to him. As soon as he went out there and threw the first pitch my mind started spinning. We didn't need this. This guy is too valuable.
"There was no energy. He was trying to compete with that. I appreciate that like I told him, but there's a bigger picture here. We need this guy to be right. Shame on me if he makes a pitch and something happens. That was going to be on me."
Colten Brewer replaced Price out of the bullpen and got out of the inning.
ESPN's Joon Lee contributed to this story.