Both round-of-16 matches will be played at El Campin Stadium. (No Colombian teams advanced to the round of 16.)
Uruguayan clubs Defensor Sporting and Nacional said they would refuse to travel should either be drawn against a Mexican team. Other South American clubs had also expressed concerns.
The decision is only the latest in response to the influenza outbreak in Mexico.
Guadalajara club Atlas has banned fans and media from attending training sessions.
Three Paraguayan players on Mexico City club Cruz Azul put their families on planes back home.
Pachuca executive Andres Fassi estimated that his club will have $500,000 in lost revenues (ticket sales and concessions) for having had to play last week's and this week's games behind closed doors.
Fassi added that 3,500 people would be out of work.
The weekend games mark the next-to-last round of the Torneo Clausura's first phase.