Waverley Mayor Paula Masselos said access to the beach could be revoked if visitors did not follow the rules.
"Swimmers and surfers will be able to safely access the water via a designated corridor [but the] beach remains closed," she tweeted.
"Please observe rules and social distancing as I really want this to work."
Nobody will be allowed to "relax or gather" on the sand, and council rangers will guard the designated entry points to ensure those entering are there to swim or surf.
Last week, Cr Masselos said the partial reopening would only apply to residents of the area.
"These measures are strictly for locals to exercise locally and if you are attending the beach to exercise, please do your exercise and leave," she said.
Neighbouring Randwick Council trialled a reopening of its beaches at Coogee, Clovelly and Maroubra for exercise only last week, but swiftly closed them again on Friday after crowds began congregating on the shore.
Randwick reopened those beaches on Saturday for the weekend, but only between 6am and 9am for swimming, surfing and jogging.
On Sunday evening, the council announced those beaches would remain open under the same conditions on Monday, but did not specify whether they would remain open for the rest of the week.
Despite the partial reopening, Randwick mayor Danny Said told those who do not live within walking distance of those beaches to stay away.
"People should not be hopping in their cars to travel to our beaches," he said.
"Our beaches are not open for leisure, they are available for exercise only. Once that has been complete, people must move on immediately.”
Across the border in Victoria, Melbourne's beaches, including the popular St Kilda Beach, were also closed to visitors last month when residents flouted social distancing rules.
While the beaches are still allowed to be used as thoroughfares, Port Phillip Council mayor Bernadene Voss said the shores remain closed to the public.
"We will follow the advice of the Victorian Government and under these restrictions, we have no current plans to reopen beaches," she said.
"The chief health officer has advised canoeing, kayaking, stand up paddle boarding, rowing and surf skiing are now permitted, subject to physical distancing restrictions and provided participants do not travel considerable distances to do them."
People in Australia must stay at least 1.5 metres away from others and gatherings are limited to two people unless you are with your family or household.
If you believe you may have contracted the virus, call your doctor (don’t visit) or contact the national Coronavirus Health Information Hotline on 1800 020 080. If you are struggling to breathe or experiencing a medical emergency, call 000.
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