The draft legislation proposes a so-called certificate of immunization, which will allow vaccinated citizens access to various sports and cultural events, cruises, and national parks.
"I don't think [the law] will pass the Congress. If it passes, I will veto it," Bolsonaro said, as quoted by the O Globo newspaper.
The bill has been approved by the Senate, the upper house, and is currently being discussed in the Chamber of Deputies.
Bolsonaro has been repeatedly accused of downplaying the pandemic risks, as he has defied coronavirus restrictions. Even though he himself contracted the virus last summer, he has repeatedly voiced skepticism over COVID-19 vaccines and only recently changed his stance, given that Brazil has been among the world's leaders in terms of cumulative infections.