Pilkington impressed for the Bluebirds before being injured in the second half, replaced by Aron Gunnarsson.
The 27-year-old left Turf Moor on crutches and Cardiff manager Russell Slade said he would be assessed when the play-off hopefuls return to Wales.
"He's in a brace so we're taking all precautions," Slade said.
"We just hope it's not too serious because he's done very well since we've converted him up there.
"I thought he was a threat all night for the two Burnley centre-backs."
Cardiff are now four points behind the Championship play-off places in seventh position after the 0-0 draw at Burnley.
Slade said his side fully deserved the point against the Championship leaders, who stretched their unbeaten run to 17 games but saw their lead at the top cut to a point.
Cardiff substitute Kenneth Zahore hit the crossbar with three minutes remaining before Bluebirds keeper David Marshall denied Sam Vokes and Ashley Barnes in injury time.
"Burnley could have stolen it in the dying seconds but on the balance of play that would have been cruel on us," Slade said.
"I thought we created some really good opportunities and probably the best chance came five minutes before those saves Marshall made.
"Zahore came on and had a wonderful chance to nick us a goal.
"The way the game was panning out I didn't think it would end 0-0. Both teams were trying to win a football match.
"There were opportunities at both ends. It was a very competitive Championship game."
Striker Anthony Pilkington will have a scan on Wednesday after suffering a knee injury in Cardiff City's 0-0 draw at Burnley.