Fans in Belfast, Ireland; Inverness, Scotland; and Sunderland, Salford and Northampton, England, will be treated to a regional premiere of his first episode of the show, which is slated to debut on television next month.
Smith is the 11th actor to play the title character on the iconic British science-fiction series. He has taken over the role from Scottish actor David Tennant.
The BBC said the first stop on Smith's tour will be Belfast, March 29.
"This is a great opportunity for the new doctor and his companion (Karen Gillan) to interface directly with the people who matter most to Doctor Who: the fans," said Piers Wenger, executive producer and head of drama at BBC Wales.
The broadcaster said premieres of the first episode of the new season are also planned for London, Manchester, Edinburgh, Plymouth and Swansea after Smith winds up his tour.