Authorities detained the migrants and the three Colombians after their boat arrived on the Costa Rican coast Saturday.
The court´s order Monday will keep the Colombians jailed while prosecutors build their case. Under Costa Rican law, suspects considered flight risks can be held in "preventive detention" for up to a year. Prosecutors can also seek extensions.
The migrants are being held at a detention center in San Jose, along with 41 other migrants from Eritrea, Ethiopia, Somalia and Guinea detained in June and July.
PM Oli off to Costa Rica