Directed by Kimberly Senior, The Who & The What began previews May 31 and was originally scheduled to run through July 13.
The cast includes Tala Ashe, Greg Keller, Nadine Malouf and Bernard White.
Akhtar won the 2013 Pulitzer Prize for Drama for his play Disgraced, which was produced by LCT3 last season. It will arrive on Broadway this fall with Gretchen Mol and Josh Radnor.
The Who & The What had its world premiere in February at the La Jolla Playhouse, where it was developed as part of the theatre's 2013 DNA New Work Series.
Here's how the play is billed: "The Who & The What tells the story of Zarina (Malouf), a brilliant and outspoken Pakistani-American writer, who goes to great lengths to please her family, even dating a convert to Islam (Keller) to please her traditional father (White). But when her father and sister (Ashe) read the manuscript of Zarina's novel about women and Islam, a confrontation ensues which threatens to tear their family apart for good."
The LCT3 staging has sets by Jack Magaw, costumes by Emily Rebholz, lighting by Japhy Weideman and sound by Jill BC Du Boff.