The speedy midfielder left a 1-0 loss to D.C. United Saturday on a stretcher with a scary looking arm injury several minutes before the final whistle.
Klopas said Mapp only suffered a dislocated left elbow, but a prolonged absence for the star winger would be a tougher blow than Saturday's defeat.
"The first game of the year, it's the last thing you want to have happen," said United midfielder Chris Rolfe, a friend of Mapp's. "Hopefully it is a dislocation and he'll be back in no time, but I just feel for him."
Jairo Arrieta scored the game's only goal in the 58th minute as the Impact played their fifth all-time match at RFK Stadium without a victory.
"It was unlucky because it was a soft goal out of nothing," Klopas said. "The fair result would've probably been a 0-0 game."
Mapp, who has been with the Impact since their 2012 MLS debut, sustained his injury on one of Montreal's best chances to tie the game and build momentum after Tuesday's dramatic CONCACAF Champions League victory over Mexican club Pachuca.
Substitute Eric Alexander sprayed the ball perfectly into Mapp's run down the right side. But after his first touch, goalkeeper Bill Hamid charged. Mapp sent his second touch into Hamid's body, then tumbled and landed awkwardly on his left arm.
Klopas said poor conditions at RFK, where significant snow fell Thursday, might have been to blame.
"I think they're going to take him to the hospital and just put (the joint) back," Klopas said. "It's just unfortunate because it was a great play for us. A great first touch, and I don't know what happened with the field. It's just an incident you don't want to see with any player."
The Impact were looking for an improved start to the season after finishing with only 28 points last year, needing 21 more to make the Eastern Conference playoffs.
The year had already begun more successfully with a run to the CONCACAF Champions League semifinals, which begin on March 18 against Costa Rican club Alajuelense.
D.C. was playing without three of its best attackers Saturday.
Fabian Espindola, last year's leading scorer with 11 goals and nine assists, served the first game of a six-match ban stemming from an incident involving officials in last year's playoffs. Fellow forwards Luis Silva (hamstring) and Eddie Johnson (undisclosed heart issue) also remained out.
United took the lead in the 58th minute on a counter-attack just moments after another of Mapp's shots forced Hamid into a save.
Arrieta raced behind the back line to reach Chris Rolfe's chipped pass and poked a calm finish beyond Montreal 'keeper Evan Bush, who had charged from his goal.
"It wasn't really miscommunication, there was just a lot of space," Bush said. "It was a situation where I either come there where it's close to a 50-50 ball, or I stay on my line and he's running at me anyway."
United sub Conor Doyle blocked Hassoun Camara's one-time effort off the goal-line in the 76th minute. Camara and others appealed for a handball and a penalty kick but it was not given.
Then Mapp got free on the right with eight minutes remaining, but blasted his shot into the body of the charging Hamid before tumbling down on his arm. It would be five minutes before he was off the ground onto a stretcher, and then a cart.
"He's been so good since he's been in Montreal," Rolfe said of Mapp, a former teammate when both played with the Chicago Fire. "So it's going to be a big blow for them if he's going to be out for an extended amount of time."