As many as 80 people are believed to have fallen ill at council-run Splashes, in Rainham, Kent, on Friday.
The centre was closed on Monday as a precaution while staff deep-cleaned the pool and added extra chlorine to the water.
Medway Council said it did not know if the outbreak was linked to Splashes, which has since reopened.
A number of people said they had to go to hospital, while the mother of a one-year-old baby said her daughter was so ill that she vomited 15 times.
More news from Kent
Sam Kemsley said her baby daughter was so ill that "after every period of sickness she was screaming in pain".
"It was terrifying," she recalled.
Johanna Grant said the "very violent" sickness came on very rapidly and affected her whole family.
In a statement, Medway Council said: "We are thoroughly cleaning the pool and changing areas and have increased chlorine levels in the pool.
"We have taken necessary precautions to stop the potential further spread of germs."
It added: "We urge customers not to visit the pool when they are feeling unwell, especially when suffering with sickness, as this would be the most likely cause of any spread of illness to other customers."
Dozens of people caught a vomiting bug after swimming at the same leisure centre, it has been claimed.