Earlier this month, UK forces helped authorities in Gibraltar who believed the tanker was carrying oil to a Syrian refinery in breach of EU sanctions. Iran says the Grace 1 was not destined to Syria.
The captain told BBC that marines made his unarmed crew kneel on the deck at gunpoint.
The MoD said the seizure complied with "international rules and norms".
On 4 July, about 30 marines from 42 Commando were flown from the UK to Gibraltar to help detain the tanker and its cargo.
The vessel's captain, an Indian national who asked not to be named, said he was radioed a police request to board his ship and lowered his ladder.
But before anyone could board, a military helicopter landed on the ship in a "very dangerous" move, he said.
The captain said the marines ignored him and instead pointed their guns and shouted "look forward, look forward".
"They didn't care whether I was master… there was no regulations… we had 28 unarmed crew. I was in a state of shock, everybody was in a state of shock.
"How do you come on a ship like this with armed forces and such brute force? For what reason?" he asked.
He said the marines could have boarded the ship and simply told him he had been arrested.
The captain agreed to speak to BBC on condition his name was not used, saying he and his crew had been advised by Indian High Commission officials to remain anonymous while legal proceedings are on-going.
Asked whether he felt there was anything illegitimate about his ship or the cargo, he said he had "followed company procedures".
The captain has since been arrested and bailed by authorities in Gibraltar.
The seizure of the tanker sparked a diplomatic crisis between the UK and Iran, which has escalated over the past four weeks.
On July 19, British-flagged oil tanker Stena Impero was seized by Iran's Islamic Revolution Guards Corps in the key shipping route, the Strait of Hormuz.
Tehran said the vessel was "violating international maritime rules”.
Both British Foreign Secretary Dominic Raab and Iran's ambassador to the UK have ruled out an exchange of the two seized ships.
Raab said: "This is not about some kind of barter. This is about international law and the rules of the international legal system being upheld."
Iranian officials said earlier that the UK seizure of the ship was an act of piracy.
While Iranian diplomat Hamid Baedinejad tweeted that it was "impossible to advance a quid pro quo or barter exchange".