The club wants to know the identity of the corporation before paying £5.75m, which was due on 30 January.
Club president Hammam has been widely seen as Langston's representative.
"Court proceedings have been issued against Vincent Tan to pay an amount of £5.75 million plus interest," said Hammam in a statement.
"This amount is due to be paid by the club and Mr Tan legally and personally guaranteed payment in the event of non-payment by the club.
"This amount is the balance due under the Settlement Agreement with Langston as unfortunately Mr Tan and the club are now in default with the legally agreed payments.
"Legally the demand is from both the club and Mr Tan, but it is for Mr Tan to honour the guarantee he has given or to use his resources to allow the club to pay its debts.
"It is to be hoped that Mr Tan recognises and executes his legal responsibilities and in so doing avoids the Club itself being dragged into the legal proceedings."
Cardiff City and Tan have yet to comment.
Before Hammam's confirmation of the litigation, Cardiff chairman Mehmet Dalman explained why they have held back the payment.
"It is bad governance not knowing who is the owner of a debt we are trying to honour," said Dalman.
He added: "Right now I want to know who it is."
Dalman said former owner Hammam had told the club he was "not" a representative of Langston.
The original debt of £24m was in the form of loan notes issued by The Langston Corporation when Hammam was at the helm of the club.
In 2013 Cardiff and Langston announced "an amicable resolution" to the longstanding debt issue.
Hammam became life president of the club as part of the settlement and his representative Michael Filiou also took a seat on the board of directors.
"Michael Filiou represents Langston on the board, but he cannot tell us who he represents," said Dalman.
http://www.bbc.co.uk/sport/0/football/31040542