The commission decided at a closed-door meeting to recall Mr Weyrauch on 23 March.
Horst Weyrauch, former financial adviser to Helmut Kohl, who resigned as CDU leader over the scandal, said he did not want to incriminate himself.
Secret accounts
Mr Weyrauch, 67, is allowed to remain silent because he is also the object of criminal investigations.
He is being investigated by judicial authorities in Bonn, the federal headquarters for the CDU during Mr Kohl's time as chancellor from 1982-1998, and Wiesbaden on secret funding in the CDU.
Wiesbaden is the capital of the western state of Hesse, whose CDU branch placed millions of dollars abroad in secret foreign accounts.
The commission's president, Social Democrat (SPD) Volker Neumann, told Deutschlandfunk radio that Weyrauch could not stonewall all questions and may possibly be fined or imprisoned if
he continues to refuse to testify.
The commission decided at a closed-door meeting to recall Mr Weyrauch on 23 March.
Mr Weyrauch is a key figure in the breaking of the scandal as he and then CDU treasurer Walter Leisler Kiep were the two men who took a suitcase containing DM1m ($500,000) from arms dealer Karlheinz Schreiber in a parking lot in Switzerland in 1991.
The investigation of Mr Kiep for tax evasion led last November to Mr Kohl admitting that he had accepted the secret contributions, part of a total of DM2m ($1m) to the party.
Mr Kohl, 69, who is also under both parliamentary and criminal investigation, returns to parliament Friday as a simple backbencher in his first appearance since the funding scandal broke in November.
It will be the start of a lengthy farewell, as Mr Kohl has already announced that he will retire in two years.
In April the CDU will choose a new party chairman since Mr Kohl's handpicked successor Wolfgang Schaeuble, himself implicated in the scandal, has said he will not seek a new term.
Secretary-general Angela Merkel is the favourite to take over and become the first woman to head the CDU.