Russia's administrative code allows prosecutors to take offenders to court and be punished for outraging public decency - punishable with fine of up to £6000 ($11,400).
One legal source in Moscow said: "It needs to be proved that the gesture was intended to be an insult and an expert has to testify in the court that it was an insult."
Williams performed three songs as part of the ceremony - his controversial single Party Like a Russian was not on the set-list.
He didn't manage to steer clear of controversy entirely, however, after raising his middle finger to the cameras as he left the pitch.
One Twitter user said: "What a joke! Watching with my kids and that happened? Wow."
Another added: "Robbie Williams is such a melt showing his middle finger!"
"Worst opening performance ever at a FIFA World Cup goes to Robbie Williams #WorldCup," another commented.
The decision to book the former Take That member to sing at the opening ceremony met with surprise when FIFA announced it on Monday.
Enraged fans took to social media to protest against the decision soon after the announcement, slamming organisers for not booking a Russian act.
One fan tweeted a picture of star with the caption: "Robbie Williams has accurately conveyed my feeling towards this World Cup."
Another said: "Robbie Williams is an extremely dubious choice to open the World Cup."
The plans for the opening ceremony at the Luzhniki Stadium had been a closely guarded secret.
Williams, described by FIFA as a "global music icon", performed at certain points throughout the scheduled 15-minute pre-tournament build-up.
The 44-year-old opened with his 1998 single Let Me Entertain You at the start of proceedings after spending time on stage with former Brazil striker Ronaldo.
Russian harpist Alexander Boldachev then took centre-stage, and a large "fire bird" entered the pitch carrying operatic performer Aida Garifullina.
She performed a duet of Williams' smash-hit Angels with the Stoke-born singer, who also closed the ceremony with the hit.
Russia won the opening game of the FIFA World Cup 5-0 against Saudi Arabia.
The star's antics will no doubt worry X Factor UK bosses after he was recently picked to lead the lineup of the show's new judging panel alongside wife Ayda Field.
According to the Mirror, the singer, 44, and his actress wife, 39, will join music mogul Simon Cowell on the panel when it returns in August in a deal rumoured to be worth around £10 million ($19m).
Former Spain captain Iker Casillas lifted the World Cup in 2010 and brought the trophy out ahead of the ceremony, as the 32 flags representing the competing nations unfurled during the the performance of Angels.
About 800 people were involved in the on-stage activities, which were held closer to kick-off than in recent finals.
Williams said opening the event to 80,000 fans and many millions all over the world was a boyhood dream, and added: "We'd like to invite football and music fans to party with us in Russia, in the stadium, or to tune in their TVs a little earlier for an unforgettable show."
