The gunman fled after opening fire on Annonciate Haberisoni as she was waiting for her hair to be done, witnesses said.
Mr Rwasa accused the government of attempting to assassinate his wife. It has not commented on the allegation.
Tensions have been rising in Burundi ahead of elections in May and June.
Mr Rwasa said at a press conference that his wife was being treated for head injuries at a local hospital, and her condition was not critical.
He would not be intimidated by Sunday’s shooting, he added.
Mr Rwasa accused the government of compiling a hit list of people to be targeted in the run-up to parliamentary elections in May and presidential elections in June.
Police said they were investigating the attack.
Witnesses were quoted in the local media as saying that Mrs Haberisoni’s life was probably saved by her hair dresser who saw the gunman taking aim and pushed her out of the way.
Mr Rwasa is a former rebel leader and an influential member of the opposition Forces for National Liberation (FNL) party.
He came out of hiding in 2013 and said he would contest this year’s election.
President Pierre Nkurunziza has not yet indicated whether he will step down or run for a third term.
He took office in 2005 following the end of a 12-year civil war, which killed more than 300,000 people.