BAA said the problem had been caused by a hardware fault which saw the check-in desks and boarding screens fail for almost three hours.
Edinburgh Airport said there was "congestion" as passengers had to be checked in manually from 07:30.
Flights were also delayed as passengers did not know which gates to go to.
The problem was fixed at about 10:00.
A man at the airport told the BBC Scotland news website he was delayed at the airport for about an hour.
He said: "My flight didn't leave until 10am because the computers were down. There were queues at the check-in desks and people didn't know where to board their flights.
"There was massive disruption."
A BAA spokesman said: "We had a slight issue this morning with the network which meant that we lost some computer services.
"It did not cause any cancellations or any great delays, but it did cause some queuing in the check in area between 7am and 9am.
"Our team were on it and, following investigation, it was found to be a hardware fault that was sorted quickly."
He added: "We saw some flights delayed by about half an hour, and congestion in the check-in area which was cleared as soon as the fault was fixed."
A "glitch" which shut down all the computer systems at Edinburgh Airport caused "massive disruption" and some flight delays.