European sailings were paused until March 31, while voyages from Jamaica and Barbados were paused until April 30, 2021.
The company said it was contacting passengers affected by the changes with options including a full refund.
A statement on the TUI website's travel updates read:
"Due to the ongoing uncertainty around travel restrictions, Marella Cruises has extended its pause in operations up to and including 31st March 2021 for European sailings and to 30th April 2021 for long haul sailings from Jamaica and Barbados.
"We’re proactively contacting impacted customers to discuss their options which will include amending to another holiday for free with an incentive or cancelling and receiving a full refund."
There is a stay-at-home order in England, Scotland, and Wales, including a ban on international travel and it is illegal to travel abroad for leisure purposes. There's also an ongoing ban on cruise ship travel for Brits.