If successful, the Thai capital would win a contract to host a race each year from 2028 to 2032, government spokesperson Jirayu Houngsub told a news conference.
"In the next 2-3 years, Thailand will have world-class competition, which we never thought would actually happen in Thailand," Jirayu said.
Tourism Minister Sorawong Thienthong told reporters the bid is worth about 40 billion baht.
In March, Thai Prime Minister Paetongtarn Shinawatra met with Formula 1 chief Stefano Domenicali and said Thailand would commission a feasibility study into hosting a Grand Prix on a Bangkok street circuit from 2028.
Hosting the race will help promote tourism, a key driver of Thailand's economy, the government has said.
Formula 1 already has a crowded schedule of 24 races around the world with four in the Asia-Pacific region, including the Singapore Grand Prix in Southeast Asia.
Thailand has an FIA-accredited track in Buriram in the northeast of the country, which currently hosts a round of the MotoGP motorcycling world championships, but the proposal is for a street race in the kingdom's capital.