James Heappey warned that an attack at Kabul airport was likely, and told people not to go there.
He said on Thursday morning UK time that the attack could happen in the next few hours.
His warning comes after the US warned Americans to avoid Kabul airport over ISIS-K threats.
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The UK Minister for the Armed Forces has warned that an "imminent, lethal attack" could happen at Kabul airport as early as Thursday morning.
James Heappey told Sky News that the "grim reality" is that intelligence has got "ever more certain" that an attack could happen at the airport or in the centers used to screen refugees looking to leave Afghanistan.
When asked by Sky News on Thursday morning UK time if an attack could happen in the next few hours, Heappey said: "Yes."
He also told the BBC on Thursday that people should stop trying to get to the airport.
"There is now very, very credible reporting of an imminent attack, and hence why the Foreign Office advice was changed last night, that people should not come to Kabul Airport, they should move to a safe place and await further instructions," he said.
"I can't stress the desperation of the situation enough. The threat is credible, it is imminent, it is lethal. We wouldn't be saying this if we weren't genuinely concerned about offering Islamic State a target that is just unimaginable."
He told Sky News the government was looking at ways to keep people safe.
"We are doing our best to look at what other alternative provisions we might be able to make, but obviously we won't be advertising those because that would simply make the alternative routes a target in themselves."
It comes after the US warned Americans to avoid traveling to Kabul airport over "specific" threats from ISIS-K, the Islamic State affiliate in Afghanistan.
Thousands of people, including foreign citizens, are still at the airport, looking to leave Taliban rule.