The Rhondda MP said the level of vitriol was higher than he had known it in 20 years in Parliament.
It comes just days after Tory MP Sir David Amess was stabbed to death at a constituency surgery in Essex.
Mr Bryant told the PA news agency: "I can't tell you much because the police have arrested this chap.
"I got off a flight from Qatar, where oddly enough David Amess was as well - we have been looking at what's happening to the refugees from Afghanistan who are all transiting through Doha.
"I got back on Saturday and the first message in my inbox was this death threat, pretty clear, so I notified the police and they have taken action."
Mr Bryant said MPs had been subjected to a "steady stream of horrific abuse" in recent years.
"It's pretty sour. It's more sour now than I've known it in 20 years," he said.
"Some of the political debates have been really vicious and sharp, especially over Brexit - though this has nothing to do with Brexit in itself - and for that matter the anti-vaxxers and so on."
Mr Bryant said his Rhondda constituency office has been targeted in the last year by an "angry mob" of anti-vaccine protesters, and the year before it was daubed with the word "traitor" over Brexit.
The former minister said he questioned "all the time" whether it was worth continuing as an MP but stressed that he felt a need to campaign on issues including tackling poverty and climate change.
Although security in Westminster is tight, Mr Bryant said MPs had to be part of their communities in the constituencies they represented.
"I don't think you can change that," he said.
"I have been doing my surgeries by appointment for some time now and we take all the sensible measures that the police advise."
The BBC reported that South Wales Police had arrested a 76-year-old man from Pontycymer on suspicion of malicious communications.
Officers were called at about 4.30pm on October 16 after reports of malicious communications being sent.