The Italian government ordered the game be played in front of an empty stadium because of the spread of coronavirus, which has particularly hit the northern Lombardy region of which Milan is the capital.
Italy has the largest coronavirus outbreak in Europe with 650 people infected and 17 deaths.
The game was closed to the public and journalists with only broadcasters allowed into the 80,000-seater San Siro.
"It's certainly a surreal situation," said Inter director Giuseppe Marotta before the match which had just a few hundred people present.
"The public is a fundamental component of football, without the audience emotions are diminished.
"But the protection of citizens must be safeguarded. We accept, albeit reluctantly, these decisions."
Ludogorets' players and staff arrived at the stadium wearing protective facemasks.
Despite their concerns, the reigning eight-time Bulgarian league winners went ahead of 26 minutes through Brazilian midfielder Cauly Oliveira.
Cristiano Biraghi pulled Inter level six minutes later finishing off a Cristian Eriksen through ball with Romelu Lukaku adding a second just before the break.
The Belgian striker picked up Alexis Sanchez's cross but his header bounced off Ludogoret's goalkeeper, before striking Lukaku's head as he lay on the ground and into the net.
Inter will also play next Sunday's Serie A game against title-rivals Juventus behind closed doors at the Allianz Stadium in Turin.