The tests had been carried out up to two weeks ago at special centres that were opened with great fanfare in the southern state, but problems with data entry meant that the travellers had been waiting for their test results for days.
Bavarian state premier Markus Soeder apologised for the problems on Thursday, promising to fix the mistakes by adding extra staff. He also said he supported his health minister who had offered to resign.
Some conservatives see Soeder as the best candidate to run for the chancellorship in next year's election, succeeding Merkel who has said she will not stand for a fifth term. Soeder has so far said he will stay in Bavaria.
Germany has managed to keep the number of Covid-19 cases and deaths relatively low compared to other European countries but there are concerns about a possible second wave of the pandemic.
On Saturday, Germany saw the biggest increase in confirmed coronavirus cases since late April, a rise of 1,415, but on Sunday the increase was just 625, although fewer cases are usually registered at the weekend.
Reuters