Most retailers, apart from larger supermarkets and off licences, will also be exempt for the whole year.
Businesses in other sectors will have their current three month exemption extended by another month.
Rates are the property taxes paid by businesses and are a significant expense in retail and hospitality.
At the start of the Coronavirus crisis Mr Murphy gave all businesses a three month rates exemption.
He had been lobbied by business groups to extend the relief and asked the Ulster University Economic Policy Centre to examine the issue.
Mr Murphy said the new exemptions would be worth £213m to businesses and brings total support from rates relief and grants to more than £700m.
He said large food stores and off licences were not part of the 12-month exemption as they had been able to continue trading, albeit with higher costs.
Mr Murphy told the assembly the extension of rates exemption was not yet fully funded, but the money would be available.
He said: “The cost for the business rates support exceeds the funding currently available. There are a number of potential sources of additional funding, and I am confident this over commitment will be met.
“We can no longer wait. Businesses need certainty now.”
Angela McGowan, CBI NI director, said the announcement will be “very well received”.
“The business rates system is one of the key economic levers the NI Executive has available to it,” she added.
“The impact of Covid-19 on how we work highlights the urgent need to consider a reform of the system as a means of driving NI’s long-term economic recovery.”
Aodhán Connolly, director of the NI Retail Consortium, said: “This welcome respite from the burden of business rates will prove to be a saving grace for some retailers as after staff costs, business rates are our industry’s biggest expense.”