Officers were seen to take staff into the reception area at Akbar's in Sauchiehall Street for questioning.
They arrived at 8.40pm, when the restaurant was packed with diners. Akbar's recently won recognition for its menu and restaurant design at the Scottish Curry Awards.
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The raid surprised onlookers and perplexed customers as police sources confirmed they were assisting in an immigration enforcement action.
One passer-by said: "It seemed to be some kind of bust, some kind of major incident. There were a couple of vans and officers are questioning people, but the premises were full and people were still eating their food inside."
Two weeks ago it emerged the Home Office was to be investigated by the equality watchdog over claims of unlawful discrimination after a wave of raids uncovered 130 illegal immigrants, including 24 at Scottish restaurants.
Indian, Bangladeshi, Thai and Chinese workers were put in detention centres awaiting deportation after the UKBA turned up at premises in Tobermory on Mull, Glasgow and Grantown-on-Spey among raids across the UK.
There were concerns some people had been targeted on ethnic grounds, a claim denied by the Home Office. It said the operations were intelligence-led.
But the Equality and Human Rights Commission (EHRC) has been probing spot checks at transport hubs and Whitehall's controversial "go home" posters on mobile advertising vans.
Twelve people, including two women, from Bangladesh, China and Thailand were arrested at three restaurants on Mull earlier this month. The Crystal Palace Chinese in Tobermory was targeted on a busy Thursday afternoon.
Akbar's, which launched last year, was the first Scottish establishment in Yorkshire-based Akbar's 10-strong portfolio, owned by Shabir Hussain, who retained his crown as King of Curry last year in the English Curry Awards.
The Home Office did not provide comment last night.