But the company has strongly denied doing anything wrong.
Its shop at St John’s Road in Birkby was raided by officers from the UK Border Agency on Thursday night.
They arrested a 27-year-old Indian man who was working in the kitchen after entering the UK illegally.
He was taken to Dewsbury Police Station for questioning before being released while the agency tries to obtain deportation documents.
It is understood he then went back to the takeaway to try to get his job back, but was given short shrift.
Domino’s has been served a notice of potential liability for employing an illegal worker.
If the company fails to provide evidence that they carried out document checks – by asking for a passport or work permit – before giving him the job, it faces a fine of up to £10,000.
But a spokeswoman for the firm said: “Our Huddersfield store is run by an experienced and competent franchisee, who carried out all the required checks.
“He was shown an Italian passport, had no reason to doubt its validity and fully complied with the Home Office requirements on checking an employee’s right to work.
“We are satisfied that he took all reasonable steps and adhered to the correct procedure.”
She added that the man’s employment had been officially terminated.
Two men were also arrested from a Leeds takeaway as part of the Border Agency swoop.
Steve Lamb, regional operations director for the UK Border Agency, said: “As long as there are illegal jobs, the UK will be an attractive place for illegal immigrants.
“That’s why we have to put a stop to employers who don’t play by the rules.
“Our officers carry out regular visits to local businesses in West Yorkshire and the message is clear – we will not tolerate illegal working.”