Harden was the runner-up for the award, with 25 first-place votes. The 25-year-old averaged 27.4 points, 5.7 rebounds and 7.0 assists while shooting 44% from the field and 37.5% from three-point range.
Harden helped lead the Rockets to a 56-26 record in the regular season. Houston will face the Los Angeles Clippers in Game 1 of the Western Conference semifinals on Monday.
Harden could face Curry in the conference finals if the Rockets beat the Clippers and the Golden State Warriors beat the Memphis Grizzlies.
"That's tough, but we're in the second round of the playoffs and I got better things to worry about and that's the Clippers," Harden said. "They're a very good team that's rolling right now and it didn't work out. But there's more of the season to continue to play."
While he's disappointed he didn't win the award, Harden said his goal is to win a title.
"That's what it's about," Harden said. "Obviously, an individual award, the MVP, is amazing. But like I said we got an amazing opportunity in this locker room and I'm not going to let one individual award affect what we got going on in this locker room. We still have a great season to play in and some great games ahead of us."
Cleveland Cavaliers forward LeBron James finished third in the MVP voting with five first-place votes. Oklahoma City guard Russell Westbrook and New Orleans Pelicans forward Anthony Davis rounded out the top five.