The 2011 winner, who was runner-up last year when the event was held in Milton Keynes, followed the likes of world number one Mark Selby, reigning champion Neil Robertson and John Higgins in failing to reach the last 16.
Trump took a 2-1 lead in the third-round clash but Selt produced half-century breaks in three successive frames to move clear.
The pair traded the next two frames to make it 5-3 and world number 35 Selt then produced a fine clearance of 128 to secure victory.
Trump told BBC Sport: “I was poor from start to finish. I always struggle here. I don’t know what the reason is. I felt flat from the start.
“I scraped through the first couple of games. I should have gone 4-4, that was a massive frame. If I could have won that one I think I could have gone on to win.”
Selt’s win saw him set up a fourth-round meeting with former World Championship finalist Barry Hawkins.
“I started off a bit slow, missing a good chance, and against a player of Judd’s calibre you need to kill every chance you get,” said Selt.
“But I managed to get a foothold and get back into it. He made some very basic mistakes and it was great news for me.”