The media mogul expressed his "regret" at what he said and added that he accepted Grant was closely involved in his child's life.
Murdoch wrote on Twitter: "Hugh Grant states that he is deeply involved in his daughter's life - I accept that, regret tweet on the matter. Apologies to both parents."
Grant was one of a number of famous faces who gave evidence at the Leveson Inquiry last year and told of the intrusive behaviour of the press towards the mother of his daughter.
This Twitter apology was Murdoch's second in 24 hours after he attempted to explain an earlier tweet in which he used the term "scumbag celebrities".
In this tweet he was referring to those who met the British Prime Minister David Cameron to discuss press regulation during the Conservative Party conference.
He tweeted: "Told UK's Cameron receiving scumbag celebrities pushing for even more privacy laws. Trust the toffs! Transparency under attack. Bad."
In an attempt to explain his choice of words, the media mogul later tweeted: "I did not say all celebrities were scumbags. Check my tweet. And apology to any who misunderstood."
Murdoch has more than 344,000 followers on Twitter and tweets on a variety of topics, including press regulation and the economy.
