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Caledonian MacBrayne says its staff have had to turn people away because their journey was non-essential.
The operator said 35 people were told they could not use the Largs, Wemyss Bay and Ardrossan service last weekend.
They have been operating a "reduced lifeline" timetable with ferries only available to help maintain supplies and services.
However, CalMac said it had seen a recent increase in people trying to travel for day trips, particularly on the Clyde.
West coast ferry operator Caledonian MacBrayne (CalMac) says it carried a total of 163 passengers on Easter Sunday.
On the same day last year it had 21,570 passengers across its routes.
CalMac, which is only providing lifeline services, says the 99.2% fall in passenger numbers shows people heeded advice to stay at home.
People can stay in their cars while travelling on some Caledonian MacBrayne (CalMac) services.
The Maritime and Coastguard Agency has relaxed rules around ferry passengers having to leave their vehicles during sailings.
The move is to help limit the spread of the coronavirus.
CalMac says passengers can now stay in their cars when travelling from Wemyss Bay to Rothesay and across the Sound of Harris, on a limited number of sailings.
It says the change does not affect any of CalMac’s larger vessels where passengers are not permitted to remain in their vehicles.
From Friday, CalMac has introduced a new reduced timetable to ensure island communities continue to get lifeline services.
West coast ferry operator CalMac will introduce a new reduced service from Friday.
It said the "essential lifeline timetable" will run for an initial three-week period as part of Scotland's "lockdown".
All islands on its 28-route network will receive a "regular lifeline service ensuring the delivery of essential goods and services", said CalMac.
In the last few days overall passenger numbers have fallen by 85% and there has been 75% fewer cars and 45% reduction in commercial traffic.
CalMac has also seen 8,000 bookings cancelled. There were 300 cancellations in the same time last year.