Investigators have linked the cases to the SSE Hydro in Glasgow, which opened in September.
Last week, NHS Greater Glasgow and Clyde said seven cases had been identified, but four more were confirmed yesterday. Ten of the people with the e.coli O157 bug live in Scotland and one in Cumbria. All are said to be recovering at home.
A statement from the health board said: "Initial investigations indicate there is a link to the SSE Hydro and an association with the consumption of burgers, but other foods items are also being considered."
Investigators are looking at the three days between January 17 and 19 at the Hydro, but advised anyone who visited the venue between January 17 and 25 and has experienced symptoms including stomach cramps, diarrhoea, nausea and fever to contact their GP.
The shows at the complex during the period were Top Gear, Del Amitri and Celtic Connections. The £125 million venue, which is to be used in this summer's Commonwealth Games, has a capacity of 12,000, meaning up to 84,000 people attended the Hydro in that period.
Eleanor Anderson, consultant in public health medicine at NHS Greater Glasgow and Clyde, said: "We are pleased all the cases are recovering at home.
"Investigations are continuing and while there is no conclusive evidence, our initial investigations have indicated there may be a link to the consumption of burgers at the SSE Hydro."
A statement from The Hydro said: "The initial review of our caterers' standard procedures have been found to be satisfactory and environmental health officers have seen nothing in their processes and practices that concerns them."