Pirin were widely criticised for their performance in a 7-1 defeat at league leaders Botev Plovdiv on Saturday and Bulgarian media reported that players from the Gotse Delchev-based side have been involved in match-fixing.
"The BFU will officially inform the competent state authorities and will ask them to place Pirin under a special monitoring," the BFU said in a statement.
Most games in the domestic championship are included on bookmakers' betting coupons.
"If the team's performance in the last match against Botev becomes a trend this season, BFU will not hesitate to expel the team from the first division to keep the principles of fair play and integrity in the championship," the ruling body added.
Pirin are 11th in the standings with one point from two matches.
Promoted to the Bulgarian top flight for the first time last year, Pirin hit the headlines in August when coach Yakov Paparkov quit a few minutes after the team won their opening match.
Match-fixing and corruption have been rife in Bulgaria for years, according to media reports, but no one has been brought to trial and the European Commission has criticised the authorities for doing little to tackle the problem.