The newly promoted Tigers had looked to be closing in on a deal for the 24-year-old, who scored 28 goals last season, as he underwent checks on Monday night.
However, the medical revealed a problem and Hull decided to pull the plug on the proposed transfer.
Asked if the deal had collapsed, disappointed manager Steve Bruce told talkSPORT: "Unfortunately, it looks like it.
"There has been a bit of a problem with his medical, which is the worst scenario for everybody concerned, and more so the boy.
"It's an awful, awful, awful situation to find ourselves in, but unfortunately the medical is not great, so it looks as if it is a non-starter at the moment.
"I think he is surprised because he has not really missed any games over the last couple of years.
"It is a blow for him and it's a blow for us, but there you go. These medicals are so stringent, things have progressed with scans and all the rest of it and obviously he has got a problem."
The collapse of the deal was confirmed by Burnley in a statement.
It said: "Burnley striker Charlie Austin will not be joining Hull City after unforeseen complications halted a proposed move to the KC Stadium.
"Austin, 24, remains a Burnley player and the club will make no further comment at his time."
The development will come as a huge blow to Hull, who agreed a deal understood to be worth in the region of £4.5million over the weekend.
No details of the medical have been revealed, but Austin has a history of shoulder problems.
Bruce will now have to turn to alternative targets, having previously expressed an interest in Celtic's in-demand Gary Hooper.
The Tigers have already completed a series of transfers with Allan McGregor, Maynor Figueroa, Curtis Davies, Ahmed Elmohamady and George Boyd having joined the club.
Bruce is hopeful of building a squad capable of competing in the top flight, despite discovering during his summer holiday that they will face a stern early test of their credentials with away games at Chelsea, Manchester City and Newcastle in their first three trips of the campaign.
Bruce said: "When I was sitting in the south of France and they [the fixtures] came out, I thought maybe I was going to sit there for a little bit longer!
"But that's what the Premier League is. We couldn't have wished for a more difficult start, to go to Chelsea in Jose's [Mourinho] first game and go to Man City with [Manuel] Pellegrini in charge. It's been all change in the Premier League.
"But the thing is, we are there, we are there again and we are competing in it. We have got to try to make ourselves competitive and we have got to find a way of trying to stay in the league.
"We have got to try to do our best and make sure we are competitive, which I am sure we will be, and make a fist of it and enjoy the challenge ahead.
"It's going to be difficult, but all that hard work of last year getting here, that's what it's all about."
Meanwhile, Republic of Ireland defender Paul McShane has signed a new two-year deal with the club.