Charity workers say there are concerns those in need of help could now be overlooked, with many opting to move elsewhere to avoid the high police presence.
Despite a visible drop in the number of beggars in Glasgow city centre, both the council and the police have insisted they have not introduced any new approach to beggars during the Games.
Last year, Glasgow City Council tried to introduce bylaws to ban public begging, but the move was rejected by the Scottish Government.
Lorraine McGrath is chief executive of homelessness charity the Glasgow Simon Community, which has an outreach service which helps rough sleepers.
She said: "People are taking themselves away, they just don't want to put themselves at risk of police attention.
"They are very aware there is a high police presence and they don't want to be subject to that.
"Some people are getting moved on [by police], but they are getting moved on rather than lifted or taken away or anything like that.
"They are going outwith the city centre, so we are looking at that.
"We do mapping of rough sleeping sites all the time, so we have extended our reach on that into areas in the west end, for instance, and will be going back and revisiting them more regularly, just to see if people are migrating into new areas."
McGrath added: "At this point in time we are not encountering major concerns, but it is very early days yet."
Patrick Harvie, Green MSP for Glasgow, said: "Any evidence of a draconian approach to begging during the Games would be extremely unwelcome and also counterproductive.
"The top priority for the authorities must always be the needs and wellbeing of those begging or homeless in the city centre, and I will be seeking assurances from Police Scotland and the city council that no other approach is being taken during this important time."
A spokesman for Glasgow City Council said it had a city-centre response team, which engaged with street beggars and directed them to services for help.
He added that no new approach or policy had been introduced by the council during the Games.
A spokeswoman for Police Scotland said: "Begging is not in itself an offence. However, anyone causing an obstruction or causing fear and alarm to the public will be dealt with appropriately by officers.
"Officers routinely engage with those who are begging to point them to the various support services which are available."