The officer has been held in prison for a month, French-language broadcaster RTS reported on Monday night, although his arrest was previously not made public.
An interim report from Valais justice authorities said at least five boys were allegedly preyed on by the policeman.
He was arrested in late January after one of the young players told his mother about the behaviour of the coach, RTS said.
The woman alerted authorities who confronted the coach, the broadcaster said.
La Nouvelliste,a Sion-based newspaper, reported online that the accused man is in his 50s.
The newspaper quotes a mother of a ten-year-old victim saying that the boys liked going to the coach’s home because he had a swimming pool.
When her son no longer wanted to go there “I realized something serious had happened,” she said.
The suspect quickly acknowledged most of the facts after being arrested on a football pitch and interviewed by investigators, RTS reported.
“In this case, as the interviews made by cantonal police specialists in the area of sexual abuse against minor proceeded, it appeared that the list of victims of the suspect never stopped getting longer,” the justice department report said.
The risk of the arrested man reoffending is high, the report said.
“In effect, his criminal behaviour cannot be considered like an isolated slip-up because the suspect often frequently abused, over numerous years, many young boys.”
Despite the apparent seriousness of the case, authorities have not said anything publicly until now.
When Le Nouvelliste attempted to get a comment from Nicolas Dubuis, local prosecutor, he replied that the justice department “does not comment on cases in progress”.