The Mavs will update Ellis' status after their Sunday morning shootaround in Boston.
Ellis is pushing to play Sunday against the Celtics, the source said, but is likely to rest at least one game.
Ellis suffered the injury late in the fourth quarter of the team's 103-81 home win Friday night against the Utah Jazz. He underwent an MRI on Saturday morning to determine the severity of the strain and traveled with the team to Boston in the afternoon.
Ellis has emerged as an explosive scoring sidekick for Dirk Nowitzki after signing a three-year, $25 million deal with Dallas this summer. He ranks 22nd in the league in scoring with 19.5 points per game while shooting 46.2 percent from the floor and averaging a team-high 5.8 assists.
Ellis is one of two Mavs who have played in all 51 games this season. He leads the team in minutes at 36.5 per game.
The rest of the road trip consists of a Tuesday game against the Charlotte Bobcats and a Wednesday game against the Indiana Pacers before the All-Star break. If Ellis sits out the entire road trip, he will have a total period of 10 days to rest before the Mavs' Feb. 18 home game against the Miami Heat.
If Ellis does not play, Devin Harris likely will take his spot in the starting lineup.
"You can't replace what he does," said Harris, who missed the first half of the season while recovering from toe surgery. "We'll have to do it by committee. He's been playing great for us."