Because of the size of the 30ft-long bomb a cargo plane with a rear door, a US Air Force MC-130, had to be used and it was pushed out of the aircraft rather than dropped from a bomb bay.
A US official told Fox News: "We kicked it out the back door."
The bomb explodes in the air and creates a massive shockwave, and the resulting "overpressure" collapses tunnels.
One official said: "It's a concussive blast. Everyone in the area is obliterated, ears are bleeding, or they're completely destroyed."
General John Nicholson, Commander of US forces in Afghanistan, said: "As Isis losses have mounted, they are using IEDs, bunkers and tunnels to thicken their defence.
"This is the right munition to reduce these obstacles and maintain the momentum of our offensive."
The US military said it did everything possible to avoid civilian casualties.
Video provided by the Pentagon showed a huge cloud of smoke after the bomb exploded.
A damage assessment was being carried out.
While the MOAB was 21,000 pounds each of the Tomahawks dropped in Syria was 1,000 pounds.
Sean Spicer, White House spokesman, said the bomb was dropped at 7pm local time in Afghanistan.
He said: "We targeted a system of tunnels and caves Isis fighters used to move around freely, making it easier for them to target US advisers and Afghan forces. We must deny them operational space.
"The US took all steps to avoid civilian casualties and collateral damage."
US officials said intelligence suggested Islamic State in Afghanistan was based overwhelmingly in Nangarhar and neighboring Kunar province.
They believe the movement has only 700 fighters but Afghan officials have estimates it at about 1,500.
Afghanistan's Islamic State offshoot is suspected of carrying out several attacks.
The Afghan Taliban, which is trying to overthrow the U.S.-backed government in Kabul, are fiercely opposed to Islamic State and the two group have clashed as they seek to expand territory and influence.
In a 2003 review of the legality of using the bomb the Pentagon concluded that it could not be called an indiscriminate killer under the Law of Armed Conflict.
"Although the MOAB weapon leaves a large footprint it is discriminate and requires a deliberate launching toward the target," the review said.
President Trump said: "Very, very proud of the people. Really, another successful job. We're very very proud of our military. It was another successful event."
"If you look at what's happened over the last eight weeks and compare that to what's really happened over the last eight years, you'll see there is a tremendous difference. Tremendous difference."
Asked if he had authorised the use of the bomb, Mr Trump said: "Everybody knows exactly what happened and what I do is I authorise my military.
"We have the greatest military in the world and they've done a job as usual so we have given them total authorisation. And that's what they're doing. And frankly, that's why they've been so successful lately."
Asked if it sent a message to North Korea he said: "I don't know if this sends a message. It doesn't make any difference if it does or not. North Korea is a problem. The problem will be taken care of."
Mr Trump said he had confidence in China's President XI Jinping to help rein in North Korea's nuclear ambitions.
He said: "I have really gotten to like and respect President Xi. He's a very special man. I think he's going to try very hard."
