Farhad Ehtesham, from Surrey, faces a race against time to be reunited with his baggage before tying the knot in Tuscany on Saturday.
The business development manager told the PA news agency the airline has failed to respond to his messages.
He and his bride-to-be, Rachel, flew from Heathrow’s Terminal 5 to Rome’s Fiumicino airport on Wednesday night.
They carried her dress as hand luggage but checked in a suitcase containing his wedding outfit, which consists of a green jacket with cream linen trousers and a gold-coloured tie.
It also has other crucial items such as presents and decorations, plus clothes for their honeymoon.
Mr Ehtesham said: “The moment we landed, we got an email saying ‘Your luggage is not there, please contact us’.
“That’s when panic starts setting in.
“You might think for clothes you can just buy others and try to claim through insurance, but it’s not that simple.
“I can’t replace a wedding outfit that was planned nine months ahead. It’s just unbelievable.”
The couple were told by airport staff in Rome that the suitcase would be put on the next British Airways flight from Heathrow on Thursday morning, but that was cancelled, and they have been unable to get further updates.
“BA’s website is really terrible because they don’t respond to any messages,” he said.
“Any phone lines just go dead.
“I tried to message them on Instagram, Facebook and so on but got no response.
“We don’t know what to do.”
Asked how he felt about the situation, he replied: “I’m stressed, I’m furious.
“I feel like I have no power to do anything about it when they don’t respond to you in any way.
“It’s one of those things you hear about, but you don’t expect it to happen to you, especially before your wedding.
“I can’t explain how infuriating it is.”
Luggage belonging to thousands of passengers flying from Heathrow this month has not been loaded on to flights.
Images have emerged of a huge pile-up of checked bags at Terminal 2.
The airport said it ordered airlines to cancel 30 flights on Thursday morning because the expected number of passengers was more than it “currently has capacity to serve”.