The stolen swing was in the destination playground which was part of a $2.5 million council spend on the park and opened in mid-2018. It was later that year recognised with the New Zealand Recreation Association's Outstanding Park Award.
There have been other acts of theft and vandalism, including the burning of sun shades.
Napier City council Onekawa-Tamatea ward member Richard McGrath says the playground has been so "fantastic" and popular that he hoped it could be extended.
But the thefts and vandalism made him wonder how far to go in providing the facilities, the popularity of which can be judged by the numbers of vehicles and people in the area each weekend.
The council is encouraging anyone with information on the activity over the weekend or who sees other suspicious activity in the area to report it to police.