It marks the first steps of the lifting of rules for close contact services since the country entered lockdown on December 20.
Welsh Government regulations say hairdressers can only serve customers with an appointment, and that services will be restricted to haircuts only.
Despite the reopening of hair salons, other businesses such as nail parlours and beauty salons are set to remain shut until at least April 12.
First Minister Mark Drakeford said on Friday that hairdressing businesses would be allowed to reopen because they have “gone through everything that is needed in order to operate safely”.
Primary school pupils will also return to classrooms for the first time this year on Monday, joining those in foundation years who returned last month and face-to-face teaching will also resume for learners in years 11 and 13.
Teachers can also invite learners in years 10 and 12 back to school in order to support their learning, while all other years will be allowed to “check in” with teachers on a limited number of days before a full school return from April 12.
It comes after Wales’ “stay-at-home” restrictions were lifted on Saturday, as the country moved to a “stay local” period, with travel restrictions expected to be eased further in time for Easter.
Wales’ seven-day case rate on Sunday stood at 39 cases per 100,000 people, the lowest of any country in the United Kingdom.
Public Health Wales said a total of 1,113,498 first doses of the Covid-19 vaccine had been given, an increase of 29,169 from the previous day, while 257,398 second doses were also given, an increase of 7,372.
There were a further 217 confirmed cases, taking the total number of confirmed cases to 206,405, while 10 further deaths took the total in the country since the start of the pandemic to 5,452.