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."
Bruce added: "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.
Source: PA
Source: PA