In a statement, the force said it had attended Hastings Mosque in St Leonards on Sunday and patrols had been "stepped up" in the area.
This incident comes amid escalating violent riots across the UK, prompting the government to announce that mosques will be offered greater protection.
On Facebook, Hastings Mosque shared a message from a local campaign group which said anti-fascist protesters had turned up to "defend" the site and "an attack did not happen."
The original post, from the Hastings branch of Stand Up To Racism, said: "On Sunday at 2pm, our friends at Hastings Mosque received a threat of an imminent attack and told us about it. After a brief chat, we agreed to call on people to come out to defend the mosque and to show solidarity to our Muslim sisters and brothers." It added that 50 people showed up within an hour-and-a-half.
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The post further stated: "We are conscious that racists are organising violent attacks on Muslims, asylum seekers and migrants."
Sussex Police said: "This incident is being treated as a hate crime and an investigation is now underway to identify those responsible."
The police have asked anyone with information about the incident to report it online or ring 101.
Source: Agencies