Terry, who originally was not expected to return to basketball activities for 10 to 14 days, said he expects to play in one of the Mavs' two games next week.
Although his conditioning felt good during Friday's practice, Terry admitted that he struggled to see while wearing a protective mask.
He planned to pick up a custom mask later in the day. He hopes to use the mask only during practices and the first couple of games after his return.
"This mask they had me wearing was like a hockey mask," Terry said. "It was terrible."
Terry, the NBA's reigning Sixth Man of the Year who is averaging 17.0 points per game, went through full contact Friday despite still lacking feeling on the left side of his face. His vision made shooting difficult.
"Oh, man, he better get used to that mask quick because that was ugly whatever he put out there," Dirk Nowitzki said, cracking a smile. "But he's a warrior. I knew he was going to come back quick."
Terry, who also returned earlier than expected after undergoing hand surgery last season, was injured in a March 3 win over the Minnesota Timberwolves. He finished that game despite knowing that an elbow from Corey Brewer broke a bone in his face.
Timberwolves coach Kurt Rambis said the elbow was inadvertent, but Terry believes a dangerous move by Brewer caused his injury.
"I definitely thought it was a dirty play," Terry said. "He's not a dirty kid at all, but in that situation, it's the move he used."