Dog walkers who flout the ban face £75 on-the-spot fines, which can rise to £1,000 if the matter goes to court.
Measures also being implemented in other parks and play areas include orders specifying no more than six dogs on lead per person.
The council has said it is not a "complete ban of dogs" but equates to "approximately 8% of all the natural space which is publically accessible in the district".
The Dog Control Orders came into force on 7 April and were introduced by the council under section 55 of The Clean Neighbourhoods and Environment Act 2005.
The orders mean the council's animal welfare officers, park rangers, and police community support officers can issue on-the-spot fines of £75 for breaches of the specific orders, as well as failure to remove dog faeces from all relevant land within the Newark and Sherwood district. Those who dispute a fixed penalty notice in court could face a maximum fine of £1,000.
A full list of the green spaces affected by the Dog Control Orders is available online.
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