The Public Health Protection Unit of NHS Greater Glasgow and Clyde is liaising with other health boards, Health Protection Scotland, the Food Standards Agency and Glasgow City Council Environmental Health to investigate these cases.
Initial investigations indicate that there is a link to the Hydro, and an association with the consumption of burgers, but other foods items are also being considered.
The unit said in a statement: "If anyone has attended the Hydro between Friday January 17th and Saturday, January 25th and has experienced, or is continuing to experience, symptoms including stomach cramps, diarrhoea (often bloody), nausea and fever they should contact a GP or NHS out of hours service."
All 11 cases are recovering at home. One case is from Greater Glasgow and Clyde, three are from Lanarkshire, four from Lothian, one from NHS Highland, one from Forth Valley and one from Cumbria.
Dr Eleanor Anderson, consultant in public health medicine, said: "We are pleased that all the cases are recovering at home.
"Investigations are ongoing and while there is no conclusive evidence our initial investigations have indicated that there may be a link to the consumption of burgers at the SSE Hydro.
"Glasgow City Council Environmental Health Officers are working closely with the vendors to ensure all appropriate food hygiene standards are being met.
"I would ask anyone who has attended the Hydro recently and who has experienced or is continuing to experience symptoms including stomach cramps, diarrhoea (often bloody), nausea and fever to contact their GP."