It is believed the mosquitoes arrived at Germany's busiest airport on a plane, according to German public health officials.
The justice department has also asked for Trump's name to be put back on the building after it was removed in June following a court order.
The hospital tells the BBC the ward door was not locked but manned with security guards, to protect the babies.
It is thought to be part of efforts to consolidate the former coup leader's control.
Eswatini is one of 12 countries, and the only one in Africa, that has diplomatic relations with Taiwan.