Michael Matheson said the vessels could be sailing next year – although he warned MSPs there are “still some questions” about whether this would happen.
He also told Holyrood’s rural economy and connectivity committee that he personally had not visited the Ferguson Marine shipyard in Port Glasgow where the two vessels were being built.
The MV Glenn Sannox ferry, which CalMac plans to use to provide services to Arran, was due to come into sevice this summer.
Mr Matheson said that it may not now be ready until 2020.
He told the committee: “Where we are with these two vessels is simply not where any of us would want to be. We want to see these vessels being utilised and on routes.
“At the present moment, the indications are they expect both vessels to be completed next year, one in the earlier part of the year prior to the summer and one later in the year.
“However, there are still some questions about their ability to keep to those timescales.”
Ferguson Marine won the £97 million fixed-price contract to build the MV Glenn Sannox and a second Hull 802 boat for CalMac, which is due to be deployed in the Outer Hebrides.
With the vessels delayed, Mr Matheson said the Scottish Government’s director of economic development Mary McAllan had contacted the shipyard earlier this month.
“She has since had to go back to them for further details around their time plan for the continued work on both the vessels and also the costs associated with them,” he told the committee.
Tory MSP for the West of Scotland Jamie Greene said: “What matters to folk is that ferries are delivered. They’re clearly way over schedule.”
He pressed Mr Matheson on the issue, asking him: “Can you give people living on our island communities any indication as to when they might expect these new ferries in operation?”
The transport secretary described the delays as being “disappointing”.
He said: “Last August we had a £3.5m resilience fund provided to CalMac to assist them in maintaining their existing vessels, to try and help improve reliability and we will provide a further £4m in this financial year in order to allow that to continue to be supported, to help mitigate some of the risks associated with vessels going off service.”