The referee was forced to abandon the Southern League match following a pitch invasion.
The club confirmed the bans came into effect immediately and said investigations were ongoing.
Two men who were arrested following the incident have been bailed.
In a statement, Hereford FC said: "Following the events that unfolded at Didcot on 4th March, Hereford FC can confirm that banning orders have been served on three supporters this week."
About 100 people were involved in the incident, which took place in the 87th minute when Hereford were leading 2-1.
A 19-year-old man from Hereford was arrested on suspicion of a public order offence, and a 19-year-old man from Hereford was arrested on suspicion of common assault.
Both men have been bailed until April.
Football banning orders have been issued to three Hereford Football Club supporters following incidents at a game at Didcot Town earlier this month, the club said.