The first of the troubled fleet entered service in April, a year late.
The trains have since suffered a series of problems, culminating in wheels being damaged on the London-Edinburgh/Glasgow service after emergency brakes were triggered.
Mr Matheson told MSPs that initial investigations showed it was caused by the "incorrect setting up of the train control management system".
Operator Serco said it was a software problem.
Several services have been cancelled since the incident at Stafford in the West Midlands early last Wednesday, including to or from Glasgow tonight and tomorrow.
The minister it was anticipated services would return to normal by the end of this week.
He said: "The primary reason for the delays has been Caf.
"It has had a marked impact on the roll out of new services."
However, a spokesman for Sleeper operator Serco, which ordered the new trains, told The Scotsman in January last year: "With trains currently in testing, we have discovered that further improvements could be made to the trains in order to enhance the guest experience.
"This is often the case with entirely new designs.
"These trains will be in service long beyond the lifetime of the franchise , and by taking a little extra time now we can ensure they will remain among the best in class for decades to come.”
Mr Matheson said today the new trains were still due to enter services on the remaining routes between Aberdeen, Fort William and Inverness to London on Sunday, 7 July.
Scottish Labour transport spokesman Colin Smyth said the new trains had been plagued with faults.
He said one third of services had run late or been cancelled since they started running on 28 April.