Without providing further details, the head of the DGS authority, Graca Freitas, told a news conference another option under consideration was to reduce the number spectators.
The director of the circuit in Portimao, in the country's southern Algarve region, said in August around 28,000 tickets had already been sold but warned fans would not be allowed in if the pandemic worsened.
Formula One announced in July the Portimao circuit would host the event for the first time.
The race is scheduled to take place on Oct. 24-25.
Freitas said the decision will take into consideration the epidemiological situation in the region where an event is happening and the type of event in question.
The start of the Formula One season was pushed back to July from March due to the pandemic, with extensive changes made to the 2020 calendar. The total number of races was cut to 17 from the record 22 originally envisaged.
Portugal, a nation of just over 10 million people, initially won praise for its quick response to the pandemic, recording a comparatively low 95,902 confirmed coronavirus cases and 2,149 deaths, but cases have crept up lately.
On Friday, the country hit 2,608 daily cases, the highest number of infections in a single day since the pandemic started, according to DGS, although testing rates have also increased. (Reporting by Catarina Demony; Editing by Andrei Khalip)