Representatives from Twitter, Facebook and Blackberry are expected to attend the meeting, which will look at how to stop people plotting violence online.
The networks were criticised during the riots after it emerged they may have been used to plan some of the disorder.
The prime minister has said police may need extra powers to curb their use.
David Cameron also said the government would look at limiting access to such services during any future disorder.
But a Home Office source said there was "no suggestion" that any of the sites would be closed down.
Networks such as Blackberry Messenger - a service which allows free-of-charge real-time messages - were said to have enabled looters to organise their movements during the riots, as well as inciting violence in some cases.
Last week, Facebook and the owner of Blackberry, Research in Motion (RIM), both said they welcomed the opportunity to discuss the matter with Mrs May. Twitter has yet to comment.'Whether and how'
Crime and security minister James Brokenshire and Lynne Owens, assistant commissioner of central operations at the Metropolitan Police, will also be at the meeting - as will a member of the National Security Council.
A Home Office spokeswoman said the talks would explore "whether and how we should be able to stop people communicating via these websites and services when we know they are plotting violence, disorder and criminality."
BBC technology correspondent Rory Cellan-Jones said one social media executive had told him the networks were keen to cooperate but that the idea of trying to block communications was "ludicrous" and had not been thought through.
Our correspondent said it was unclear whether the hour-long meeting would produce any major new policies.
Facebook says it has already prioritised a review of content that is "egregious during sensitive times like the UK riots" with the hope of being able to take down such material more swiftly.
A number of people have appeared in court in recent weeks for organising or attempting to organise disorder on social networks.Perry Sutcliffe-Keenan and Jordan Blackshaw were jailed for four years for incitement on Facebook
Jordan Blackshaw, 21, from Marston, Cheshire, and Perry Sutcliffe-Keenan, 22, from Warrington, Cheshire, were jailed for four years for online incitement.
Blackshaw had created a Facebook event entitled "Smash Down Northwich Town" while Sutcliffe-Keenan set up a Facebook page called "Let's Have a Riot in Latchford". Both have said they will appeal.
Meanwhile, 21-year-old David Glyn Jones, from Bangor, north Wales, was jailed for four months after telling friends "Let's start Bangor riots" in a post that appeared on Facebook for 20 minutes.
And Johnny Melfah, 16, from Droitwich, Worcestershire, became the first juvenile to have his anonymity lifted in a riot-related case for inciting thefts and criminal damage on the site. He will be sentenced next month.Plotting violence
In the aftermath of the riots, which spread across England's towns and cities two weeks ago, Mr Cameron said the government might look at disconnecting some online and telecommunications services if similar circumstances arose in the future.
"We are working with the police, the intelligence services and industry to look at whether it would be right to stop people communicating via these websites and services when we know they are plotting violence, disorder and criminality," he told MPs during an emergency session of Parliament.
Tim Godwin, the Met police's acting commissioner, also said last week that he considered requesting authority to switch off Twitter during the riots.
However he conceded that the legality of such a move was "very questionable" and that the service was a valuable intelligence asset.
Currently, communications networks that operate in the UK can be compelled to hand over individuals' personal messages if police are able to show that they relate to criminal behaviour.
The rules gathering such queries are outlined in the Regulation of Investigatory Powers Act (RIPA).