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 ($1.23 billion).
In March, Thai Prime Minister Paetongtarn Shinawatra met with Formula One 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.