The incident occurred during a match between local team Alianza and the Santa Ana-based team Fas at Cuscatlán Stadium.
The match was subsequently suspended.
President Nayib Bukele described the event as "unprecedented", and said an "exhaustive investigation" would be launched.
Police had earlier said that seven men and two women were among the dead, with all the victims over the age of 18.
The disaster reportedly occurred after a large number of fans tried to enter the venue after the gates had been closed.
Officials believe some fans had been sold fake tickets, and said that an investigation was under way.
Footage shared by local media appeared to show fans attempting to pull down barricades at the stadium's entrance.
A livestream of the match posted on YouTube shows the match being suspended after an apparent commotion in the stands. People are later seen being carried away by emergency services on stretchers.
Fans are also seen waving their shirts at people on the ground to try and cool them down.
"It was an avalanche of fans who overran the gate," a volunteer with the Rescue Commandos first aid group told journalists. "Some were still under the metal in the tunnel. Others managed to make it to the stands and then to the field and were smothered."
President Bukele said "everyone" will be investigated, including teams, managers, stadium officials, the league and the federation.
"Whoever the culprits are, they will not go unpunished," he said in comments posted to Twitter by his press secretary.
Officials also said that 90 people were being given medical attention, and that men, women and children had been treated for "multiple traumas".
Luis Alonso Amaya, from the Civil Protection of El Salvador, said that about 500 people had been given medical treatment, with many transferred to hospital.
Health minister Francisco Alabi said that most of those injured are in a stable condition and that there have been no reports of deaths from hospitals.
The Salvadoran Soccer Federation said that all national level football matches on Sunday would be suspended. It also said it regretted what had happened and voiced support for the victims' families.
El Salvador's health minister, Francisco Alabi, tweeted that the government had deployed ambulances from nearby hospitals to the stadium with the injured being sent to different public institutions for treatment.
Mr Alabi also called for the public to cautiously evacuate the area to make it easier for medical teams to carry out care.