Videos on social media showed a group of hooded men throwing chairs and smashing glasses while Hammers fans sat in the bar on the city’s Rytirska Street.
A statement from Czech police said three people had been injured in the incident which also saw a police offer attacked.
“We have restricted the personal freedom of 16 people and we are currently investigating the whole incident,” the statement said.
More than 10,000 officers are on duty in the Czech capital with major security concerns around the game given the vast numbers of supporters who have travelled without tickets.
UEFA have promised a beefed up security presence at the Eden Arena, which seats just shy of 20,000 fans, the governing body desperate to avoid a repeat of the carnage that marred last season’s Champions League final between Liverpool and Real Madrid in Paris.