The incident took place in a central area of the Ukraine capital on Sunday evening, less than 48 hours before England's World Cup qualifier against the former Soviet republic.
Pictures of blood-spattered pavements quickly circulated on social media sites, drawing condemnation from all quarters.
The attack came a year after England fans encountered no problems in the country during Euro 2012.
Hodgson was stunned by the attack and said that he hoped all the injured made a quick recovery in time for the game in the Olympic Stadium.
"We deplore that, everyone deplores that and I'm certain people in Kiev deplore that," manager Hodgson said.
"I don't know the circumstances. It's unfortunate these things can happen when football fans get together.
"The atmosphere here last year was remarkable and nothing like that happened.
"I'm sad it's occurred and I only hope our fans are not going to be put off by that and I hope the fans aren't so badly injured they can't attend the game."
It is understood the three people concerned have now left hospital and have opted not to co-operate with police investigations.
Around 2,000 England fans are expected to attend Tuesday night's game though and police have reported a relaxed atmosphere in a city where there were no problems last year despite a much larger number of supporters for two games in Euro 2012.
"We are aware of what happened last night and we will be going round most of the major bars, including this particular one to make sure there are no problems," said Rachel Barber, head of the UK police delegation in the Ukraine.
"We would urge supporters to enjoy themselves but to do so without upsetting anybody.
"I am pleased to say that currently, the atmosphere in the town is good, so in that sense what happened last night was out of the blue.
"Sometimes there can be an element of bravado on social media and you can never legislate for something happening but hopefully the England fans will just have a good time in what is a fantastic city."
Ukraine head coach Mykhaylo Fomenko later apologised to the England fans about the attacks.
"We are very sorry about this," he told a press conference at the stadium where the two teams will face off in front of a sell-out 70,000 crowd.