Burn landed on his back after jumping for a header in Saturday's 1-0 home Premier League win over Arsenal and did not return for the second half after suffering a spinal injury.
"Dan Burn will be out for some time. Long-term problem, a couple of months is a speculative number. He landed on his spine. A huge blow," Howe told a news conference on Monday.
"It's not just one position we're losing, we're losing his ability to play centre-back as well. But it's something we have to roll with," he added, referring to Burn's ability to also play at left-back.
Dortmund won 1-0 at St James' Park a fortnight ago, moving up to second place level on four points with Newcastle who are now third. Paris St Germain are group leaders with six points.
Howe's side will be looking for a win at Signal Iduna Park despite being hampered by injuries to key players including Sven Botman, Alexander Isak, Harvey Barnes, Elliot Anderson and Jacob Murphy as both teams battle for a place in the last 16.
"It's built in me, I think every game is a must-win and the term is probably overused in football," Howe added.
"But it's the only way that we prepare. We prepare to win every game, we never have anything else in our minds and we will prepare to win this one."
Newcastle, sixth in the Premier League, have enjoyed back-to-back victories after beating Manchester United 3-0 in the League Cup fourth round last week before the win over Arsenal.
