Also, Real Madrid lost again while suffering its worst scoring drought.
Messi scored and walked off injured in the first half of Barcelona's 4-2 win over Sevilla at Camp Nou Stadium, while Real Madrid players and coach Julen Lopetegui were jeered off the field after they lost to Levante 2-1 at Santiago Bernabeu Stadium.
Messi was taken to a clinic, and Barcelona said he broke the radial bone. At the least, he will miss the Champions League match against Inter Milan on Wednesday, and the clasico against Barcelona next Sunday.
"We will notice his absence," Barcelona coach Ernesto Valverde said. "But we've played without him in the past. We will be prepared to overcome this."
Messi was trying to reclaim the ball when he ran into the back of a defender and fell in the 17th minute. Trying to cushion his fall, his right elbow bent badly and he was in visible pain. Doctors wrapped his arm with bandages and the playmaker tried to continue but gave up.
"We shouldn't let Messi's injury affect us," defender Gerard Pique said. "We have a team good enough to do well in the matches that we have ahead."
Messi scored their second goal with a shot from outside the area in the 12th, about 10 minutes after Phillipe Coutinho opened the scoring. Luis Suarez added the third by converting a second-half penalty kick.
Sevilla replied through Pablo Sarabia, Ivan Rakitic increased Barcelona's lead in the 88th, and Sevilla netted again thanks to Luis Muriel in injury time.
Barcelona struggled more than the scoreline showed, with goalkeeper Marc-Andre ter Stegen having to make a pair of remarkable double-saves, but the result was enough to give Valverde's team a one-point lead over surprising Alaves.
Sevilla, which had won four in a row in the league, including 3-0 against Real Madrid, dropped to third place, two points off the lead.
Atletico Madrid, which drew at Villarreal 1-1, also was two back after nine matches.
Real Madrid was four points behind Barcelona, in fifth place.
REAL MADRID'S DEBACLE
Real Madrid fans ran out of patience after seeing their team suffer its worst scoring drought and lose for the fourth time in five matches.
Fans loudly jeered after Madrid reached 481 minutes without finding the net in the loss to Levante, which entered the game with the league's third-worst defense.
Levante scored early with goals by Jose Luis Morales in the sixth minute and Roger in the 13th after a penalty awarded following a video review. Marcelo pulled one back in the 72nd.
Madrid began the match without Gareth Bale and Karim Benzema, who are coming off injuries. It still created enough chances, striking the woodwork three times and having a goal by Mariano Diaz disallowed for offside in the final minutes. Marco Asensio also had a first-half goal disallowed by VAR.
Madrid finished with 70 percent possession and more than 30 attempts.
Local media immediately questioned whether Madrid should fire Lopetegui before the clasico next weekend at Barcelona or give him a chance to try to save his job against the rival.
"Football matches are won by scoring goals and not according to who deserves to win," said Lopetegui, who is only three months into his stint with the club after being fired from Spain's national team.
Before the clasico, Madrid hosts Viktoria Plzen on Tuesday in the Champions League to try to rebound from a 1-0 loss at CSKA Moscow.
Atletico struggled against Villarreal and goalkeeper Jan Oblak pulled off difficult saves to keep Diego Simeone's team from defeat.
Luis Felipe put Atletico ahead in the 51st and Mario Gaspar equalized in the 65th.
Villarreal, 14th in the standings, remained winless after six home matches in all competitions this season.
Valencia couldn't manage more than 1-1 against struggling Leganes at home, being held winless for the fifth time in six matches.
Valencia has only one win this season, 1-0 at Real Sociedad two rounds ago.
Jose Gaya scored in the 85th minute to keep the hosts from losing after Gerard Gumbau put Leganes ahead with a second-half penalty kick.
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