A Conservative member of Parliament asked Straw about a ban during questioning in the House of Commons, the Daily Mail reported.
"I do not believe that this is a matter which should be the subject of the criminal law in which we were expecting the police to remove these items of apparel from women who choose for religious or cultural reasons to wear them," Straw said.
Straw bars women from covering their faces in his constituency office in Blackburn.
A recent poll found a majority of British residents favor bans on burkas and niqabs in some public places, including banks, airports and universities. About one-third would support banning them from being worn in public completely.
The public is more tolerant of the hijab or head scarf, which covers the hair but not the face.