The decision has been taken by the governing body due to concerns over the coronavirus outbreak in Italy. Two people have died in the country while reports say dozens more have tested positive.
Bulgarian champions Ludogorets had demanded assurances that it was safe to travel to Milan in a statement released on Sunday, calling on UEFA to provide swift clarification.
Inter, who won the first meeting 2-0 thanks to goals from Christian Eriksen and Romelu Lukaku, will stage the return fixture without any fans present inside the famous venue.
"Earlier in the day, the Milan club sent a letter to Ludogorets, announcing that the city's health authorities allowed the match to be held without fans," a statement on Ludogorets' website read.
"The European headquarters informs Ludogorets that it will demand the decision of the Milan medical authorities. UEFA also announces that it is monitoring the situation in Northern Italy and will react immediately if changed.
It was confirmed by Inter in a statement on Monday that no spectators will be present for the encounter.
Inter's clash with Sampdoria was one of four Serie A fixtures to be postponed on Sunday, while there are doubts over whether their upcoming trip to Juventus will go ahead.
Italy prime minister Giuseppe Conte has said all of the top-tier Italian games, including the blockbuster showdown in Turin, could be called off due to the virus, which originated in China.