The watchdog will investigate whether the work and pensions secretary broke the rules on MPs' conduct.
Downing Street said Gordon Brown had "full confidence" in Mr Hain, who has said his failure to declare the donations was an innocent mistake.
But Plaid Cymru has called for Mr Hain, who is also Welsh secretary, to resign.
The Conservatives have held back from calling for Mr Hain's resignation, pending the outcome of the investigation by standards commissioner John Lyon.
But Tory work and pensions spokesman Chris Grayling said: "If he gets severely criticised by the standards commissioner I think there will be very real doubts about his future."