Speaking in Germany ahead of Newcastle's crunch Champions League match with Borussia Dortmund on Tuesday, Howe confirmed the "long-term" injury and said: "Dan will be out for some time I think."
The manager said two months was "a speculative number for us".
"He landed on his spine, he's got a problem at the base of his spine."
"It's a huge blow."
Burn picked up an injury in Saturday's 1-0 win over Arsenal.
"He's been gigantic for us for lots of different reasons" said Howe, "it's not just one position we're losing, but his ability to play centre-back as well."
Newcastle lost the reverse fixture in England 1-0, thanks to a first-half goal from Dortmund midfielder Felix Nmecha.
The English side currently sit third in the group behind second-placed Dortmund, with the two teams equal on points.
