Leicester led through Demarai Gray's early opener when Brady was hurt in an accidental collision with Harry Maguire, the Republic of Ireland international's momentum carrying him into a heavy clash with the centre-back as he shaped to shoot.
Brady was in obvious pain and was taken off the field on a stretcher with his left leg in a brace, but Dyche said Burnley need to wait for more news on the winger, who scored a brilliant winner at Bournemouth on Wednesday.
Dyche said: "He's gone off to hospital, so we need to find out more before I can give the full facts. It looks more serious than not serious to me
"It's a blow because Robbie has been excellent lately. But we've had knocks like this before, so we'll rethink things and move forwards."
Sean Dyche confirms that Robbie Brady was taken to hospital following the injury suffered at Leicester City.— Burnley FC (@BurnleyOfficial) December 2, 2017
SD: "We're awaiting news, but we think it's more likely serious, than not serious."
Defeat at the King Power Stadium was only the second time Burnley have lost away from home in the Premier League this season, with Dyche satisfied by the effort shown by his side in their third game in a week.
"It was a close affair, I thought we were excellent in the first half," Dyche told Sky Sports. "We conceded a sloppy goal with the lad taking a chance and getting a bit of fortune, a gamble moment, but fair play to him that sometimes gets you a goal.
"After that we dominated the first half, we were very good. Especially from set pieces we had two or three great chances, one golden chance. Second half it was more of a ding-dong which maybe suited them so they could counter and we knew that.
"We had a golden moment right at the end where [Ashley Barnes] doesn't quite make contact and you might get a scruffy one, an own goal."
CLAUDE: “We could have been more clinical in the second half and perhaps we would have had more goals, but to win with a clean sheet is always satisfying.” #LeiBur— Leicester City (@LCFC) December 2, 2017
Victory for Leicester was their third under new manager Claude Puel, who has seen his side take 11 points from his six games in charge, the Foxes losing only to Premier League leaders Manchester City in that run.
"On the pitch it was a difficult game, they are sixth and with confidence," the Frenchman said. "We saw this in the first half.
"It was important to win this game. I think it's a good result and a good reward for the players and their hard work on the pitch.
"It's encouraging to see different players and it was a good thing for Demarai that he scored. We need to continue to improve all of the time. We need to keep this positive attitude."