The two groups pelted each other with stones and set vehicles alight on Saturday following several days of tensions, police said.
Paramilitary forces have been deployed in Vadodara, which is 110 kilometres from Ahmedabad.
"Police have arrested over 40 people in connection with the communal riots in Vadodara," said senior state government official SK Nanda.
"The number is likely to increase as combing operations are still on," Mr Nanda, additional chief secretary for the home ministry, told news agency AFP.
The ban on phone services would remain in place until September 30 in a bid to stop the clashes spreading and to defuse tensions, officials said.
Tensions have been mounting since Thursday after photos that were circulated on social media incited communal tension.
Prime Minister Narendra Modi, who is currently in the United States and is set to meet with US President Barack Obama, won the seat of Vadodara at the national elections in May. However, he chose to represent Varanasi in Uttar Pradesh in the Lok Sabha. The by-election for his seat in Vadodara was won recently by the BJP.