Jahed Choudhury, 24, married Sean Rogan at Walsall Register Office and shared his story on YouTube.
However, he told the Victoria Derbyshire Show he had been threatened online and in the street.
But the couple said they had also received messages of support and would continue to share their story.
Since their ceremony Mr Choudhury said the couple had received death threats online and abuse on the streets.
"The worst [messages] say 'the next time I see you in the streets, I'm going to throw acid in your face'.
"Even if I walk down the streets, I have people spitting on me and calling me pig - all the nasty stuff. I just keep walking."
The couple said they had not yet reported the incident to police and were considering whether to do so.
Mr Choudhury said he had also received "amazing" support from his online followers, including people who said the couple had inspired them to come out.
"I've been brought up Muslim and the Koran mentions you cannot be gay and Muslim. But this is how I have chosen to live my life. I will never get rid of my faith."
Mr Choudhury said he had attempted suicide in the past but added his family had been "really supportive" since he came out.
He has now set up a YouTube channel where his story received more than 5,000 views, and says he was motivated to speak out online to encourage support for gay people from religious backgrounds.

Finance Secretary Mark Drakeford said the idea was "attractive" and could help tackle poverty and inequality.
Supporters said it would help unemployed people who fear taking a job would lead to cuts in their benefits.
But Patrick Minford from Cardiff University's Business School said it was "not a workable scheme".
Under Universal Basic Income (UBI) everyone would receive the same sum of money regardless of whether they work or not.
There would be no requirements to show an individual is looking for a job either.
In Scotland the policy has support from across the political spectrum, with feasibility work under way ahead of possible pilot schemes in Glasgow and Fife.
Jamie Cooke, head of the RSA think tank in Scotland, told the BBC's Sunday Politics Wales programme: "Moving from a system where you aren't working to a system where you are, you won't face those penalties, you retain your consistent payment.
"You're given the security to be able to choose to work... or training, or to set up your own business in a way that is beneficial to you."
However Prof Minford, who was an adviser to former prime minister Margaret Thatcher, told the programme: "This is not a workable scheme because it's far too expensive.
"It creates a tremendous tax, a disincentive for the average person further up the income scale who's paying for it all."
Mr Drakeford told the assembly earlier in January he found the idea of UBI "attractive in the way that it can simplify and support people who currently have to rely on a very complex set of part-time work, part-time benefits and so on".
But he added: "The political world will face a job of convincing the public about the merits of the scheme."
Asked if he was worried by Mr Drakeford's comments, Prof Minford replied: "It's quite worrying for Wales.
"I'm hoping Wales won't go the same way [as Scotland] towards this sort of extremely expensive socialist experiment".

Trago Mills, which runs three stores in Cornwall and Devon, was granted planning permission in 1999 but work was stalled by several issues including access and land reclamation.
Now, work officially gets under way next to Cyfarthfa Retail Park on Friday.
The development is due to be completed by spring 2018.
It will include a new store, cafe and garden centre, as well as warehouse, offices and parking.
There are also plans to develop the site further with a petrol station and leisure facilities.
The company was founded in the 1960s by Mike Robertson, father of current chairman, Bruce Robertson.
He said: "Whilst rather later than anticipated, having first acquired the former Butterley Brickworks site in the mid-90s, we're delighted to be starting work on the Merthyr store.
"Once completed, our new store will be a bold and complementary addition to the thriving retail environment already existing at Cyfarthfa."
A man thought to be one of the first UK Muslims to have a same-sex marriage said people have threatened to throw acid in his face since the ceremony.
[NEXT_CONCEPT]
Paying everyone in Wales a universal basic income would be a "worrying and extremely expensive socialist experiment", an economist has warned.
[NEXT_CONCEPT]
Work is starting on a long-awaited £40m retail and leisure complex in Merthyr Tydfil, set to create 400 jobs.