Hicks will undergo an MRI on Saturday to determine the severity of the injury and whether it might require him to miss time.
"I feel good right now, so we'll see how it goes and see what the result says," Hicks said after the game.
Hicks, who began the fourth by singling off Red Sox starter Chris Sale's 91.4 mph fastball, was replaced at first base by pinch runner Brett Gardner.
Gardner remained in the game in center.
Hicks said that during pregame warm-ups, he felt a little pain in his hamstring but he assumed it was a cramp. He was able to make it through the first three innings with little issue before the injury started to flare up during his second plate appearance.
"I got one inning, two innings, three innings, then finally during that last at-bat, it started cramping up on me," Hicks said. "I was trying to stay in the game, but my body language was saying that I should get out of the game."
The injury came a little more than a week after Hicks was sidelined for three games with left hamstring tightness. Hicks had trouble with that hamstring during the opener of the Yankees' penultimate regular-season series, at Tampa Bay. He made it into only the fourth inning of that game before coming out.
Hicks eventually returned in time for last weekend's final three games of the regular season at Boston, as well as Wednesday's AL wild-card game.
The pain of this hamstring tightness isn't as prominent as what he felt in the left leg, Hicks said.
It was during his noticeably slow jog up the first-base line following his fourth-inning single that Hicks appeared to be favoring the leg. He tried to stay in the game as the next batter, Giancarlo Stanton, hit. But after manager Aaron Boone and athletic trainer Steve Donohue came out to evaluate him, Hicks was removed.
"It kind of sucks to be able to come out of this game," Hicks said.
New York could replace Hicks on its ALDS roster, but he would also have to remain off the championship series roster if the Yankees advance.
Tyler Wade, a utility player who was left off the Yankees' ALDS roster, could be a possible replacement. Although he primarily plays second base, Wade also has played the outfield. He is currently at the Yankees' facility in Tampa, Florida, continuing to work out with other fringe-roster players who could be emergency adds.
Greg Bird, another reserve who didn't make the Yankees' ALDS roster, is in Boston with the team.
Hicks leaves ALDS Game 1 with hamstring injury
Aaron Hicks rips a single to right field and has to leave the game after suffering a right hamstring injury.