The 22-year-old Russian international was detained in the early hours on Wednesday after being stopped by police near the city centre following Tuesday's 1-0 win over Shakhtar Donetsk in the Champions League.
"It's not the first time he's broken the rules," Zenit spokesman Dmitry Tsimmerman told Reuters.
"He's been warned before so this is probably the last time we're going to deal with it. In any case it will be up to the club to make a decision on his future with the team.
"He didn't play on Tuesday so if he decided to celebrate our victory he did it on his own," Tsimmerman added.
Ionov was released by police after paying a 2,000 rouble ($65.20) fine and will face a court hearing next week.
Early this season Zenit coach Luciano Spalletti demoted the gifted midfielder to the reserves for undisciplined behaviour. He was later recalled to the first team.
Ionov has one international cap after making his Russia debut in a friendly against Qatar in March.
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