The move comes as public health officials confirmed four new cases of COVID-19 in the Cayman Islands.
Premier Alden McLaughlin said the recent crowding at supermarkets raised the risk of community transmission of the virus.
He said the new arrangement had been devised to control crowds and urged families to designate only one shopper and not to bring children to the store.
Anyone whose last name starts with the letters A-K will be able to shop Monday, Wednesday or Friday.
Anyone whose last name starts with letters from L-Z will be able to shop Tuesday, Thursday or Saturday.
The new system comes into place Monday and applies across all three islands.
Government insists there is more than enough food and other supplies in stock at all grocery stores and that the supply chain to the islands remains intact.
But officials are concerned that the large crowds gathering at supermarkets could undermine the regulations they have put in place to contain the spread of the coronavirus through the community.
McLaughlin said enforcement of the new regime would be a joint effort between police and supermarkets, but he warned the public, “If you know tomorrow is A-K, and your name is Levy, you shouldn’t turn up at the supermarket.”
The premier urged compliance with all the measures of the soft curfew.
He said police had stepped up their surveillance and he urged everyone to stay home unless they were exercising for 90 minutes or going to the store, pharmacy or gas station. He said a similar alphabet-based split-shift could be introduced for all the measures in the soft curfew if police did not get full compliance and co-operation with the regulations.
“We have had an increase in the number of positive cases by four and we expect that number is going to continue to rise,” McLaughlin warned.
He said all but one of the cases had been linked to travel, but there was no certainty that the virus had not spread through the community.
“The only way we can reduce our risk of contracting the virus is to stay away from as many people as possible. Stay home Cayman,” he said.
Governor Martyn Roper backed the new measures and noted that 2.4 billion people across the world were now under some kind of curfew.
“A third of humanity is now in lockdown,” he said.
Open hours: 6am to 6pm
6-7am: Designated hour for senior citizens, disabled people and pregnant women
5-6pm: Designated hour for essential workers
Opening hours: 7am to 6pm
7-8am: Designated hour for senior citizens, disabled people and pregnant women
5-6pm: Designated hour for essential workers
Opening hours: 7am to 6pm
7-8am: Designated hour for senior citizens, disabled people and pregnant women
5-6pm: Designated hour for essential workers
Opening hours: 6am to 6pm
Front of line service is available for senior citizens, persons with disabilities, and pregnant women during operating hours.