Quarterback Art Schlichter of the Baltimore Colts was suspended indefinitely yesterday by National Football League Commissioner Pete Rozelle for betting on at least 10 NFL games last season and for associating with gamblers.

In a prepared statement, Rozelle said that several psychiatrists have diagnosed Schlichter, a 23-year-old former all-America at Ohio State, as a compulsive gambler and that he has entered an undisclosed hospital for treatment "by a team of physicians and therapists qualified in the care of compulsive gamblers."

Rozelle's action was the first public confirmation that Schlichter bet on NFL games or that he was a compulsive gambler since it became public last month that Schlichter called the FBI field office in Columbus. At that time, Schlichter told the FBI he lost $389,000 to four Baltimore area men in the first three months of this year.

The four men were charged with violating federal gambling statutes and pleaded innocent to all charges in U.S. District Court in Columbus last month. Their pretrial hearing is scheduled for Monday afternoon in Columbus and the trial is scheduled to begin June 6. Schlichter's attorney said he would be available to testify then.

Rozelle said he would review Schlichter's suspension before the 1984 season. If he is reinstated, Schlichter would have to fulfill the remaining terms of his Colts contract, according to Joe Browne, an NFL spokesman. It is believed Schlichter has two years and an option year remaining on the contract.

A highly placed NFL source also indicated that the investigation of Schlichter did not uncover gambling by other players in the league.

In Columbus, Jack Chester, Schlichter's attorney, said his client is in the first week of what is expected to be at least three to four weeks of intensive inpatient treatment. Chester said that Schlichter then will receive outpatient treatment.

Chester said Schlichter is under the care of Dr. Robert Custer, chairman of the Department of Treatment Services of Mental Health and Behavorial Sciences at the Veterans Administration in Washington, D.C. Chester said that Schlichter is in a private hospital and that it is neither in the Washington area nor Ohio.

Custer's prognosis for a complete recovery is "very optimistic," Chester said.

According to Chester, NFL, NFL Players Association and NFL Management Council sources, Schlichter's illness is covered by insurance. But no one was able to say for certain whether the insurance would cover all his bills.

Chester said that Schlichter had been "betting on everything, except his own games" and the problem began before the Colts made him the fourth player chosen in the 1982 draft. "From what I understand, this didn't come on all of a sudden with him coming to the Colts," Chester said. " . . . It was there before he came to the Colts." Chester declined to be more specific.

Sources close to the NFL investigation said yesterday that Schlichter bet "several hundred dollars or more" on the NFL games and that he did a great deal of parlay betting. They declined to say how much was meant by "more." Said Chester, "Betting on NFL games was so mixed in with the total picture that . . . dollar-wise, it was minimal."

In his statement, Rozelle said, "Schlichter acknowledged that he placed sizable bets on at least 10 NFL games during the 1982 season and postseason . . .

"I accept his statement that he has never bet on or against his own team, attempted to improperly affect the outcome of any games or accepted money or anything of value from those who might have been interested in doing so."

Schlichter is the first NFL player suspended for gambling or associating with known gamblers since Paul Hornung and Alex Karras received indefinite suspensions prior to the 1963 season. Five other players were fined at that time. The suspensions against Hornung and Karras were lifted before the 1964 season. Chester said he was disappointed with the commissioner's ruling.

"I would have preferred that the commissioner would have said, 'Arthur should undergo intensive therapy and when he is pronounced fit to play by medical people, then he would be allowed to play.' Commissioner Rozelle has a responsibility to Arthur, and he recognized it; but he also has a responsibility to the NFL."

Chester said no decision has been made whether Schlichter would fight Rozelle's action in the courts. "I have not had a chance to review the legal implications for myself or for Arthur," Chester said.

NFLPA Executive Director Ed Garvey issued a statement saying the players union will monitor Schlichter's suspension and in which he accused Rozelle of a double standard in dealing with players and owners.

"We hope that the commissioner will use his authority to thoroughly investigate and take appropriate action regarding the activities of team owners as well," Garvey said. "Rozelle has been silent thus far in the matter of Baltimore Colts team owner Robert Irsay's outrageous threat that he would 'get John Elway' or direct his players 'to get Elway.' We have yet to hear from the commissioner on the numerous reports that Philadelphia team owner Leonard Tose lost millions in gambling debts last year.

"The union feels Rozelle is operating under a double standard and will not protect the integrity of the game if he does not judge management actions in the same light as the actions of the players."

In Baltimore, the Colts issued a brief statement:

"We accept the commissioner's judgment . . . We only hope that Arthur's rehabilitation from his problem is successful. We look forward to having him back with the Baltimore Colts when the National Football League decides he can return to the club."

Schlichter was the Colts' third-string quarterback last season, behind rookie starter Mike Pagel, a fourth-round draft choice, and veteran backup David Humm. In his rookie season, Schlichter completed 17 of 37 passes for 197 yards, with two interceptions and no touchdowns.

The Associated Press quoted USFL Commissioner Chet Simmons as saying the new league would be interested in Schlichter even though he did not know Schlichter's contract obligations.

"I would have to make a determination if playing is as strong a rehabilitative force as just being rehabilitated and suspended," Simmons said. "If his inability to play would be a deterrent to his rehabilitation, then I would very seriously be interested in talking to him."