Taylor headed Newcastle ahead in the 15th minute of the Premier League clash at St James' Park after meeting Jack Colback's corner.
However, the 28-year-old centre-back had to be replaced in the second half after landing awkwardly when jumping to head the ball.
Newcastle assistant manager John Carver, who took charge of the encounter, subsequently confirmed that Taylor is set for a long spell on the sidelines.
"We think Steve Taylor has snapped his Achilles tendon, which is disappointing," Carver said.
"He's a great lad, it was great for him to get the goal. You could tell when he landed it was something to do with the calf or the Achilles and it's not looking good."
The build-up to the New Year's Day encounter was dominated by the news that Newcastle manager Alan Pardew would not be in the dugout as he gets set to take the vacant role at Crystal Palace.
There was plenty of drama on the pitch as well in a thrilling encounter that saw Newcastle take the lead three times through Taylor, Colback and Moussa Sissoko only to surrender the advantage on each occasion as a comical Paul Dummett own goal and strikes from Danny Ings and George Boyd earned Burnley a point.
Carver even accepted Newcastle were fortunate to take a point against a Burnley side who hit the woodwork four times.
"I don't think I have been involved in such a game of, to use the old cliche, two halves," he added.
"We controlled the game and played really good football in the first half but the second half was pretty awful.
"I thought we had got out of jail [with Sissoko's goal] but they should have won the game. They were the better team over 90 minutes. They caused us more problems than we did them."
