Messi will now miss Barca's Champions League game at home to Inter Milan on Wednesday, as well as the season's first Clasico four days later against Real Madrid.
A Barcelona club statement read: "Tests carried out on Leo Messi have confirmed that he has a fracture of the radial bone in his right arm. He will be out for approximately three weeks."
It means Messi is also set to sit out a La Liga trip to Rayo Vallecano on November 3 and the Champions League return match against Inter Milan in Italy on November 6.
|Lionel Messi will miss the Clasico against Real Madrid and the Champions League double-header with Inter Milan (AFP)|
He could return for the league game at home to Real Betis on November 11.
"It is clear it is a blow," Barca coach Ernesto Valverde said. "We know what he gives us and we know what he does to the opposition.
"We have to prepare ourselves, it is clear we are going to notice the loss of Messi but we have players that can cover."
Messi scored before going off in the 26th minute of Barca's 4-2 win over Sevilla at the Camp Nou, which sent them back to the top of La Liga.
He fell to the ground following a tussle with Sevilla's Franco Vazquez and, as his right hand tried to cushion the landing, his elbow appeared to buckle.
Philippe Coutinho had opened the scoring and Luis Suarez's penalty made sure of victory before a three-goal flurry in the final 11 minutes.
Pablo Sarabia and Luis Muriel twice reduced the deficit to two for Sevilla, either side of a sweeping volley from Ivan Rakitic.