Bryant tried to beat out a double play, but he ended up slipping on first base.
The 27-year-old will undergo an MRI on Monday, and the Cubs expect to have more information before Tuesday's game, according to Jordan Bastian of MLB.com. Bryant will travel with the team to Pittsburgh.
The club said initial X-rays didn't reveal a fracture, adds Patrick Mooney of The Athletic.
Trainers had to help the three-time All-Star off the field.
Bryant is hitting .282/.381/.522 with 31 home runs in 146 contests this season.
Cubs first baseman Anthony Rizzo also recently suffered an ankle injury, but he made a surprise return to the lineup after missing just four days.
Chicago entered Sunday's action three games behind the Milwaukee Brewers for the NL's second wild-card spot.