Following the play, Infante was checked on by assistant athletic trainer Mike Kozak and his teammates, but remained in the game.
Infante fielded a grounder for the final out of the fourth and singled in the bottom of the frame for his third hit in as many at-bats.
Emilio Bonifacio, who started at shortstop, said he first thought it was Infante's nail that was bothering him until he saw his double-play partner swing the bat with his finger sticking out.
"He couldn't grip the ball, it was really hard," Bonifacio said. "During the inning, he told [manager Jack McKeon] he couldn't keep playing, and that's when I figured ... because [for] Omar [it] is hard to come out of the game."
Wes Helms replaced Infante at second.
"He was getting three hits a game, and he gets hurt," Marlins left fielder Logan Morrison said. "That guy's tough, though. He got a base hit with a broken finger. That's pretty impressive."
Infante hit .409 with two homers and three RBIs in his past five games. He was the only Marlins player to appear in every game this season.
"He was carrying us offensively. He's done a great job the last week hitting the ball like he did last year," McKeon said. "He got a lot of key hits for us, and you know what kind of defense he plays. He's superb out there on the field."
With shortstop Hanley Ramirez listed as day-to-day with a left shoulder sprain -- following his dive on an over-the-shoulder catch Tuesday night in New York against the Mets -- Bonifacio started Friday night's game at short and Greg Dobbs was at third base.
Thurston, who got the start at second and was batting seventh, has spent parts of six seasons in the Majors, last playing in the big leagues in 2009 as a member of the Cardinals.
In New Orleans, the 31-year-old was batting .316 with nine homers and 44 RBIs in 103 games. He had started 86 games at second base.
To make room for Thurston on the 40-man roster, the Marlins transferred Scott Cousins to the 60-day DL with a lower back strain. He has been out since June 13.
"[Infante's] a gamer. He likes to play. That's why you say when it's 15 days, you kind of almost put money he'll be ready to go," McKeon said. "They said two weeks, but they said it wasn't that bad of a break. Knowing Omar -- he can't get back before two weeks -- but he should be ready to go."