The move follows three days of violence in Marseille involving Russian and English supporters and local French gangs.
There has also been trouble in Nice where local youths reportedly attacked Northern Ireland and Poland fans.
And on Sunday there were reports of fighting between German and Ukrainian hooligans.
FA chief executive Martin Glenn condemns the behaviour of some England fans as `deplorable` but says it was a much wider problem.
The French interior minister Bernard Cazeneuve said: "I have asked for all necessary measures to be taken to prohibit the sale, consumption and transport of alcoholic drinks in sensitive areas on match days and the day before, and on days when fan zones are open.
Saturday`s unrest, which left more than 30 people injured, prompted UEFA to warn both Russia and England that they risked being thrown out of the tournament if there was any repeat.
The ban will include public areas, as well as shops and off-licences, Cazeneuve said.
Senior local officials can also ban bars and cafes from serving drinks on their terraces in containers that can be used as missiles.
"The events which took place in Marseille yesterday evening are unacceptable. Unacceptable for the authorities, unacceptable for society, unacceptable for football lovers," Cazeneuve said.
Alcohol to be banned in `sensitive areas` at Euro 2016
13 June 2016
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Alcohol will be banned in fan zones and other "sensitive" areas at Euro 2016, the French government has announced.
