Sussex Police said officers were working with Adur and Worthing Council.
UK Power Networks have been informed.
A spokesman said: "We have closed Brooklands Par 3 Golf Course in Worthing today (11 August) after reports of two dogs suspected to have been electrocuted after entering the pond.
"We are asking the public not to go to this area of the park until further notice and apologise for any inconvenience caused."
A spokesman for West Sussex Fire and Rescue confirmed crews were assisting police at the scene.