Damian Green must explain why half the immigration desks at Heathrow Airport were closed on Monday morning despite long queues of passengers waiting to enter the country, a Labour MP said.
Keith Vaz, chairman of the Commons Home Affairs Select Committee, said he was appalled at the length of queues at 7am and that he would ask the Immigration Minister to explain the situation to MPs on Tuesday.
His comments come just over two weeks before the Olympics start and after shadow home secretary Yvette Cooper said it was a disgrace that international athletes were waiting longer than two hours to pass through immigration control.
Mr Vaz said: "I was appalled by the length of queues in the immigration hall this morning. It is now two months since the Immigration Minister promised additional resources and better management.
"The worst aspect was that half of the immigration desks were simply not opened even though the Border Force had prior knowledge of all flight arrivals. This creates additional security pressures with luggage piling up in the baggage hall. We look forward to hearing the Immigration Minister's explanation for this tomorrow."
Queues at Heathrow Airport were more than an hour for non-EU passengers, despite a 45-minute target, when Mr Vaz visited Terminal 4 at 7am, his spokeswoman said.
On Sunday, Ms Cooper said many of those forced to wait in long queues were Olympic athletes, who will be arriving ahead of the opening ceremony on July 27 to acclimatise to UK conditions.
A leaked memo reveals that tourists arriving from outside the European Economic Area are repeatedly waiting longer than the 45-minute target time to pass through passport control. Meanwhile, European visitors are waiting up to 40 minutes when it should take less than 25 minutes to have their documents checked.
But Mr Green said the Government's actions to tackle queues "have resulted in real improvement over the last two months - including consistently hitting our targets on UK and EU passengers and reducing waiting times across the board".
A spokesman for airport operator BAA said: "Immigration waiting times for passengers during peak periods at Heathrow in the last few days have been unacceptably long and the Home Office should be delivering a good experience for regular passengers as well as for Olympic visitors. Immigration is a matter for the Home Office."