The species has venomous spines on its gills and dorsal fin and usually stings humans while buried in the sand beneath shallow water.
Stings typically increase in incidence during the summer months although the true figure often goes unrecorded as many victims do not report their injuries.
Weever fish stings can cause severe pain which is more acute than that caused by a bee or wasp sting.
Hornsea Coastguard said: "We are aware of several reports that people and children have been stung by weever fish in the Hornsea area.
"Weever fish can often be found all along our coastline and other areas in the UK, so please follow safety advice. Wearing suitable footwear on the beach and in the sea will reduce the risk of being stung.
"If you are stung by a weever fish please follow NHS guidance, call 111 or go to the nearest NHS Urgent Treatment Centre (the nearest to Hornsea are in Beverley or Bridlington). If you are at a beach with RNLI lifeguards on duty you can seek assistance from them.
"For any life-threatening or severe reactions to a sting listed in the NHS guidance please dial 999 and ask for an ambulance."
Pain increases in severity around three minutes after being stung and other symptoms include itching, swelling, heat, redness, numbness, vomiting, joint aches, abdominal cramps, increased urination and tremors.
In rare cases the stings can cause severe reactions such as seizures, gangrene and unconsciousness.
In most cases the pain will decrease within hours but discomfort can last as long as a week.
First aid treatment consists of immersing the affected area in hot water, which will accelerate denaturation of the protein-based venom. The use of hot water will reduce the pain felt by the victim after a few minutes. Any broken spines should be removed from the wound.