Quinn, who broke the finger and damaged a tendon on his throwing hand in a win over Buffalo last week, will visit Andrews in Birmingham, Ala., for a second opinion on Tuesday, a person with knowledge of Quinn's injury said on condition of anonymity because of the sensitivity of the situation.
Quinn is seeing Andrews on his own initiative, the person said Monday night.
ESPN.com, citing an unnamed source, first reported Quinn's trip to see Andrews.
Quinn, who recently took over as Cleveland's starter, was benched by coach Romeo Crennel late in the third quarter on Sunday after throwing his second interception in a 16-6 loss to Houston, the Browns' third straight defeat at home.
Crennel made the switch to Derek Anderson because of misreads made by the second-year QB, who broke the tip of his finger when he banged it on a Buffalo defender in the first half of the Browns' 29-27 win. After the Texans' loss, Quinn refused to blame his injured finger for his poor performance.
However, Crennel said Monday that Quinn had trouble throwing the ball because of the injured tendon.
"It makes it tough for him to spin it [the ball] the way he wants to spin it," Crennel said.
Quinn thought he only bruised his hand last week but complained of soreness following practice on Wednesday. Tests revealed a small fracture on the tip of his finger and Quinn was examined at the Cleveland Clinic by a specialist, who cleared the former Notre Dame star to make his third career start Sunday.
Quinn finished 8-of-18 for 94 yards before Crennel brought in Anderson, a Pro Bowler last season who lost his job three weeks ago. Crennel said he based his decision on Quinn's performance and his injury.
"I decided to make the change to try to get the spark," Crennel said. "Some of that had to do with some misreads, some of it had to do with my knowledge of the finger situation and so I decided to make the change."
Anderson went just 5-of-14 for 51 yards, but the Browns dropped three of his passes, one a TD to wide receiver Braylon Edwards, who had three more drops and leads the NFL with 18.
Crennel's swift switch to Anderson stunned many of the Browns and puzzled Quinn, who said afterward that he "didn't really have any inclination I was on such a short leash."
Although he was replaced, Quinn has not lost his starting position, Crennel said. Quinn is expected to start Sunday's game against the Indianapolis Colts.
"We were not able to win the game unfortunately, so it becomes an issue," Crennel said. "But it's not an issue, because he [Quinn] is the quarterback. We like the things he has shown us since he's taken over the starting job: his composure, his leadership, he doesn't get rattled. We like all of that."