The diagnoses were made after the Lisbon club played a Primeira Liga match against Benfica on Saturday that started with only nine Belenenses players on the pitch because of a COVID-19 outbreak.
Only seven players returned to the field after halftime, and the match was abandoned two minutes into the second half with Benfica leading 7-0.
Belenenses defender Cafu Phete tested positive for COVID-19 after returning from international duty in South Africa on Nov 17, and he and 12 others at the club were confirmed on Monday to be infected with the Omicron variant, which was first detected last week in southern Africa.
By Monday, more than a dozen countries had reported cases of the variant, which the World Health Organisation said carried a very high global risk of surges.
DGS chief Graça Freitas told broadcaster SIC that nearly all Belenenses players had been vaccinated against COVID-19, adding that all their high- and low-risk contacts would get tested.
A club spokesman said most of those infected were asymptomatic or had mild symptoms, and that 44 players and staff were self-isolating and waiting to repeat tests.
The Benfica and Belenenses presidents said that, had they not played the match, they risked being penalised for an "unjustified absence". They blamed the league and DGS for not postponing the game.
The league, which earlier said it did not receive a formal request to postpone the match, was on Monday investigating if the match had complied with health rules.
DGS said it was not up to the health authority to postpone the game.
Portugal, which has one of the world's highest COVID-19 vaccination rates, last week announced the return of curbs to slow the epidemic's spread. It additionally suspended flights to and from its former colony Mozambique from Monday to combat the variant.
Belenenses played against third-division club Caldas on Nov 21. A Caldas spokesman said they would test their players.
A Benfica spokesman said none of their players were in isolation as the Belenenses players they faced on Saturday were not considered high-risk contacts. Benfica's next match is scheduled for Friday.