The midfielder's exact misdemeanour remains unclear, although it has been suggested the incident occurred during the Championship club's training camp in Slovenia last week.
Bullard is believed to have returned to England with his team-mates before being ordered to stay away from City's training ground for two weeks.
The 32-year-old was omitted from Hull's 2-1 pre-season victory at non-league Winterton Rangers last night. After the friendly manager Nigel Pearson was asked about Bullard's suspension, and told the Hull Daily Mail: "I've got no comment to make on that."
When contacted on Thursday afternoon, no-one at the club was able to comment on the allegations.
Bullard has two years remaining on his ?45,000-a-week contract at the KC Stadium and has repeatedly been linked with a move away from East Yorkshire over the past 12 months, spending the second half of last season on loan at Ipswich.
Source: Team Talk
Source: Team Talk