The European Tour, and the players who took part, came under scrutiny last year for staging an event in Saudi Arabia because of its human rights record, especially with the tournament taking place three months after the killing of journalist Jamal Kashoggi.
Dustin Johnson won the inaugural event and returns this year along with Mickelson, Brooks Koepka, Tony Finau, Patrick Reed, and European stars Henrik Stenson, Shane Lowry and Sergio Garcia.
Woods and Rory McIlroy are among those not playing.
"I understand the politics behind it," Woods said Tuesday. "But the game of golf can actually help heal all that, too. It can help grow that. There are also a lot of other top players that are going to be playing that particular week. It's traditionally not a golf hotbed in the Middle East, but it has grown quite a bit."
Mickelson said in a statement released by tournament organizers that he watched Johnson win last year and thought the course looked like an interesting challenge, along with mentioning how it could help grow golf in the region.
All the top players are paid hefty appearance fees, which is allowed on the European Tour.
Mickelson later replied to criticism on Twitter by saying, "I understand those who are upset or disappointed. You'll be OK. I'm excited to experience this for the first time."
Mickelson previously played in Abu Dhabi in 2011 and 2014.
Woods has a long history in the Middle East, first playing the Dubai Desert Classic in 2001. He played Dubai eight times, most recently in 2017, and won twice. He also played twice in Abu Dhabi.
"I remember going to Dubai for my very first time and seeing maybe two, three buildings on the skyline when you tee off on No. 8," he said. "Now there's a New York City skyline back there. The game of golf has grown. There's only been a few courses when I first went to Dubai, now they're everywhere; same with Abu Dhabi and maybe eventually in Saudi Arabia."
Tiger Woods Design is building Trump World Golf Club Dubai, which is scheduled to open next year.
Meanwhile, the tournament chairman of the Waste Management Phoenix Open said he was disappointed by Mickelson's decision to play in Saudi Arabia the same week as the PGA Tour event he has played the last 29 years and won twice.
According to ESPN, Tim Woods said at the tournament's "Tee-Off Luncheon" on Tuesday that Mickelson has been a big part of the tournament and he hopes that it isn't his last time playing the Phoenix Open.
"But I also understand. I mean, at the end of the day, this is a business and we respect his decision for him and his family that he needs to go and make sure that he still provides in that arena," Tim Woods said. "So, it's hard to hold a guy down or at fault for making a decision like that."