In the lead-up to the poll, opposition leader Raila Odinga had sounded warnings about the computerised voting system which failed when the last poll was held in 2013.
He's now alleging hackers gained access to the electoral commission's computer using the identity of the commission's IT manager, Chris Msando, who was killed last month.
In response to the allegations, Kenya's Independent Electoral and Boundaries Commission says it will investigate, says chairman Wafula Chebukati.
"Whether it's hacked or not, those are aspersions which have been cast, those are allegations. As a Commission, we shall have our own investigative system to kick in. We shall come up with a methodology as to finding out whether or not those claims are correct."
The Commission has released polling data on its website, showing incumbent president Uhuru Kenyatta is leading with 54.3 per cent of the vote.
Mr Odinga currently has a 44.8 per cent share, with almost 97 per cent of the votes counted.
The Commission says those figures are preliminary.
Under Kenya's laws, the Commission is required to announce the results within seven days.
Election monitors were deployed across Kenya, including 130 from the European Union.
EU chief monitor Marietje Schaake welcomed the large voter turnout.
"I think scars from the past have underlined the importance of democracy and peaceful co-existence. I think it is a very welcome step to see wide and diverse participation in these elections. And I really hope that the rights of all Kenyans will prove to have been respected."
Former US Secretary of State John Kerry is also in Kenya to monitor the election, for the Carter Centre.
He's warned against people jumping to hasty conclusions.
"People need to be patient, people need to let this process work through and not jump to conclusion at this point in time. I think Kenyans have the opportunity here to show Africa and the international community an election that followed the rules, followed the process and honours everybody's vote."
Meanwhile as angry protests have erupted in pro-opposition areas of the western city of Kisumu and in pockets of the capital, Nairobi.
Although the violence remained largely contained, Kenyans were nervously hoping to avoid a repetition of the killings that followed a disputed 2007 presidential poll, when some 1,200 people died.
