Under the state requirements, shops and salons can only serve customers by appointment only, waiting areas must be closed, customers and workers must wear face masks, chairs must be at least 6 feet apart, and scissors and other tools must be disinfected between customers.
Lamont first said barbershops and hair salons could reopen May 20, but he pushed the date back after some shop owners and employees said they wanted more time to prepare.
Other owners and workers were frustrated by the postponement.
Casinos in the state are open as well, as both Mohegan Sun and Foxwoods had soft re-openings over the weekend.
They are open to the public Monday with social distancing and other safety measures in place.
The governor also increased the limits on social and recreational gatherings to 10 people indoors and 25 people outdoors. The previous limit was five people per gathering.
Phase two is tentatively set for June 20, and phase three could follow four weeks after that.
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