The team will determine after the surgery whether Olsen will be placed on injured reserve with the expectation he would return later in the season, the source added.
Olsen was injured in the first half of Sunday's home opener against the Buffalo Bills.
"My understanding is things went well, and we'll see from there,'' Panthers coach Ron Rivera said.
Rivera said the team hasn't discussed what to do with Olsen's roster spot. He called timetables on Olsen "purely speculation.''
But Rivera has discussed with his staff ways the Panthers can replace a player who has led the team in receptions and receiving yards the past three seasons. He liked that quarterback Cam Newton targeted nine different players in Carolina's 9-3 win over Buffalo.
He compared the situation to the 2015 season, when Newton spread the ball around more after losing wide receiver Kelvin Benjamin to a season-ending knee injury in training camp.
Newton went on to an MVP year, with a career-best 35 touchdown passes, and the Panthers led the league in scoring.
"That's huge,'' Rivera said. "When you start using all the weapons, it's tough to say, 'OK, who should we focus on? Who should be our primary focus?'
"If we can do that and be successful, that stuff carries over just like it did in 2015.''
Rivera also liked what he saw out of backup tight end Ed Dickson, who had two catches for 26 yards against Buffalo.
"We're not going to change the offense because Greg's out,'' Rivera said. "We're going to do things that we do. One of the worst things you can do now is all of a sudden say we have to change all the things we've put in.
"Ed is more than capable.''
Olsen is a three-time Pro Bowl selection who became the first tight end in NFL history with three consecutive 1,000-yard receiving seasons. Before the start of the season, the Panthers added $2 million in incentives to his contract based on receptions, receiving yards and postseason honors.
Olsen had one catch for 10 yards against Buffalo before the injury. He had two catches for 18 yards last week in a 23-3 season-opening victory at San Francisco.
Olsen has started 81 consecutive games, the third-most in team history behind safety Mike Minter (94) and offensive tackle Jordan Gross (84). His streak is also the second-longest among active tight ends, behind only Dallas' Jason Witten (164).
Information from ESPN Panthers reporter David Newton was used in this report.