The actress previously worked with Akhtar on the road movie Zindagi Na Milegi Dobara
A source told The Times of India: "Katrina Kaif was pleasantly surprised when Farhan gave her the guitar. It was a belated birthday gift for her. Farhan rarely has a party at his place. This party happened impromptu.
"He thought of gifting Katrina a guitar since when the Zindagi cast had gone for their road trip, Farhan had carried his guitar along and Kat really liked it.
"She had expressed her desire to learn guitar quite a few times. Katrina was overjoyed at the gesture."
Zindagi Na Milegi Dobara follows three best friends on a road trip in Spain who are forced to sort out their differences and change their relaxed attitude to life.
Akhtar recently spoke out against rumours about his personal life, saying that his children were upset over media speculation about romantic links to actresses such as Deepika Padukone.
Watch the trailer for Zindagi Na Milegi Dobara below: