The wooden pergola from Greyfriars Community Centre on Christchurch Road in Ringwood is used to offer the children some shade and a place to relax while playing outside.
But at some point between May 31 and June 1, the sun shelter was stolen from the centre.
It is valued at £2,000 and Hampshire police are now ramping up their investigation into the incident by appealing to the public for witnesses.
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Officers did not realise information on how many people were potentially involved with stealing the large piece of furniture.
A spokesperson for the force said: “If you were in the area at the time and witnessed anything of the incident, please contact 101 and quote incident number 44250240089.
“We’d also like to hear from you know of the pergola’s current whereabouts, or if you have any footage of the incident, including CCTV, dash cam, mobile phone or doorbell camera.”
