Last season's American League most valuable player, Don Mattingly, became baseball's latest millionaire yesterday, agreeing with the New York Yankees on a one-year contract for $1,375,000.

The agreement came shortly after midnight, the club said, avoiding Mattingly's salary arbitration hearing scheduled to begin at 9:30 a.m.

Mattingly, who earned $325,000 in base salary and $130,000 in bonuses last season, had asked for $1.5 million in arbitration and the Yankees had offered $1.25 million. "The Yankees met us halfway. We felt they were making the effort," said Mattingly.

After pitcher Dwight Gooden of the New York Mets agreed to a $1.32 million contract last week, the Yankees offered their first baseman the same salary. Though he rejected the Yankees' offer, Mattingly said Gooden's salary was not a factor in his financial considerations.

"I stand on my own two feet," he said. "But both of us being in New York, I think it's a natural comparison for the media to get into."

In his second full major league season, Mattingly was the league's RBI leader with 145 and batted .324 with 35 home runs . . .

In Boston, right-hander Dennis (Oil Can) Boyd also avoided an arbitration hearing by agreeing to a one-year contract with the Red Sox worth more than $350,000. Dennis Coleman, Boyd's agent, said the deal is worth about $375,000, with incentives.

Boyd, who earned $140,000 last season, had filed for $495,000 in arbitration, with the club countering with $315,000.

The Red Sox had other good news as later in the day an arbitrator ruled in their favor in the case of catcher Rich Gedman. He had had been seeking $1 million for the '86 season, but was awarded $650,000. He earned around $400,000 in 1985, said his agent, attorney Bob Woolf, who added he is "terribly disappointed" by the ruling.

Later still, Boston second baseman Marty Barrett, who batted .266, won a $435,000 contract from an arbitrator, $110,000 more than the Red Sox had offered. He played for $272,500 last year.

The Red Sox face baseball's biggest arbitration case Friday with third basemen Wade Boggs. After winning $1 million in arbitration last year, he is seeking $1.85 million for 1986. The Red Sox have offered him $1.35 million . . .

Hank Aaron, who hit a record 755 home runs during his 23-year major league career, said at a meeting of the Durham (N.C.) Sports Club that players' drug problems and high salaries have discredited professional baseball.

"The drug problem has been here in professional sports a long time," said Aaron, who directs the Atlanta Braves' farm system. "Unfortunately, it has been swept under the rug. Nobody wanted to face it."

Aaron said rules must become stricter to keep the sport free of drug users. "One way to get rid of them [drug users] is on the first offense to knock them out of the game," he said. "There should be no second chanch."