The reason is the mutated British variant of the coronavirus, which has tightened restrictions between countries.
Leipzig had applied for an exemption for Liverpool's players and staff ahead of the quarter-finals on February 16, but was refused by the German interior minister, reports the news agency DPA.
What happens to the match is not clear.
Leipzig can turn to Uefa and request that it be played on a neutral level.
Another option is to turn the game around and let Liverpool be the home team on 16 February.
The return meeting will be played on March 10.
In that case, Leipzig's squad would have to be quarantined on their return to Germany.
Uefa monitors developments and is prepared to advance matches.
April 2 is the last date to be able to play a round of 16, writes AP.
Manchester City's meeting with Borussia Mönchengladbach away on 24 February is also in danger.