The decision was announced after holding a COVID-19 review meeting on Monday.
In a series of tweets, Kumar said that all essential and non-essential shops can operate in Bihar till 7 pm, while public parks and gardens will remain open from 6 am to 12 pm.
However, the Chief Minister said that the night curfew will continue in the state from 9 pm to 5 am, adding that people must continue following appropriate COVID-19 norms, including usage of masks and practising social distancing, to ensure that cases do not rise again.
Complete lockdown in the state was imposed on May 5 after the state witnessed a surge in COVID infections.
Bihar, one of the worst-hit states in the country, has been reporting a decline in daily COVID-19 cases.
As per the health update by the Union Ministry of Health and Family Welfare, Bihar currently has 3,189 active COVID-19 cases.