Rollie Fingers, the American League's most valuable player of 1981, incurred a separation of his left shoulder yesterday at the Milwaukee Brewers' Sun City, Ariz., training base.

The San Diego Padres, training in Yuma, Ariz., meanwhile reported that left-hander Chris Welsh, a regular in their pitching rotation, had broken a bone in his leg in a first-base collision Friday and will be out of action approximately six weeks.

The Brewers said Fingers will be out two to three weeks. But the club could not certify that Fingers will be available for the opener at home against Cleveland April 6.

Right-handed reliever Fingers, also last year's AL Cy Young and Fireman of the Year awardee, was injured in a warmup exercise before an exhibition game. Playing "flip," in which players hit the ball to each other with their hands, he fell on his shoulder.

In yet another Arizona camp, that of the Oakland A's in Phoenix, the team physician said Eddie Mathews, the Hall of Fame player serving as a batting instructor, has tuberculosis. The illness was described as treatable and curable by Dr. Thomas E. Richmond, and he said Mathews could be back on the job in a week to 10 days.