The 21-year-old was subbed out of the Tigers' loss to the Blues in the first quarter after hurting his left hamstring at the 12-minute mark.
He pulled up suddenly on the city-side wing and grabbed at a spot high on his left leg before being helped from the field.
While the tendon is not off the bone, he has been scheduled to have an operation to repair "disruption" that will sideline him from running for at least a month.
"He'll be able to jog after four weeks but then the running progression would be quite slow," elite performance manager Peter Burge told AFL.com.au.
"In my experience of these, they're probably doing controlled football type stuff in rehab at about anywhere from eight to 10 weeks.
"I think he'll get a really good conditioning block with the rehab phase with the injury, and I can't see it really affecting his pre-season too much."
The first to four-year players will return to training in the first week of November, with Conca – who remains out of contract with the Tigers – to be close to a full program around that time.
He is likely to be in a position to merge into the main training group in December.
Burge said the severity of the injury surprised the Richmond fitness staff given Conca has not had problems with his hamstrings before.
He also said the tendon could have been left to heal on its own, but surgery would likely produce a better outcome.
"He's the last person we expected that to happen to, and so early in the game," Burge said.
"It's pretty disappointing because it was unexpected. There was nothing leading up to it that indicated that he had any sort of issue.
"Tendons behave in a very random manner sometimes.
"It may have healed without surgery but the surgeons just thought it would be easier to go in and do a little repair just to make sure it heals well,” Burge added.
"Just getting a couple of stitches makes it nice and strong, and it's actually almost a quicker way of getting them going again."
The procedure is similar to the one defender Dylan Grimes had in November after his own battles with hamstring problems.
Burge said there were no other major surgeries scheduled with the Tigers poised to be in good shape when they returned to training.
"We'll be in a better position this year," he said.
"When I started in October, November last year, we had quite a few guys who were having things done.
"We've got a lot less this year and we'll be in a stronger position with our pre-season."