The club - relegated from the Football League in 2012 - were reported to owe £116,000 to HM Revenue and Customs, although owner Andy Lonsdale had promised to invest £1 milllion.
Lonsdale, though, was late in arriving at court on Friday, and the judge elected to proceed with the winding up order.
Herefordshire Council reacted to the news by revealing their plans for repossessing the club's Edgar Street grond.
"As Hereford United Football Club (1939) Limited is in the process of being wound up and a liquidator will be appointed, this action triggers the council’s right as landlord to forfeit the leases," read a statement. "The council will now pursue this and seek to gain formal repossession of all three sites leased to the club.
"Once the ground has been secured, the council will consider the appropriate process for procuring a new tenant to ensure the continuation of football.
"The council is unable to seek immediate possession of the ground, there is a prescribed legal process which the council must adhere to.
"At this point in time we understand that this process is likely to take a couple weeks."
