Clarence House said, in light of the red weather warning, the away day would be rescheduled.
The Met Office has issued the highest level of alert, stating there could be a “danger to life” as a result of extremely strong winds.
The red weather warning, meaning a high impact is very likely, covers the coastline of Devon, Cornwall and Somerset as well as the south coast of Wales and will be in effect from 7am until 12pm on Friday.
A spokesman for the prince said: “Following official guidance, the Prince of Wales’s visit to Newport and Swansea on Friday February 18 will not go ahead due to the dangers posed by Storm Eunice.
“In the interests of public safety, these engagements will be postponed with a view to rescheduling at a future date.”
The heir to the throne is facing his own storm after the Metropolitan Police launched an investigation on Wednesday into a cash-for-honours scandal involving Charles’s charitable foundation.
Charles was due to travel to Newport, Swansea and Ammanford – his second public appearance since catching Covid for a second time.
Police have launched an official investigation into the alleged cash-for-honours scandal linked to the Prince’s Foundation.
Charles and his former most trusted aide Michael Fawcett were reported to officers over the claims.
The trust, which is based at Dumfries House in Ayrshire, is not run by Charles, who is not a trustee.