The 29-year-old from Penang secured nearly 60% of the popular vote for his free-kick in the Malaysian Super League against Pahang state in February.
He was presented with the trophy by Brazilian football legend Ronaldo.
Others in the running included players like Marlone and Venezuelan midfielder Daniuska Rodriguez.
Also at the inaugural ceremony, held in Zurich, Cristiano Ronaldo was named the world's best player, beating old rival Lionel Messi to the title.
Faiz, who plays with the Penang FA team, spoke of his surprise at his win and dedicated the prize to his family, friends and country.
"I'm extremely happy because I didn't expect it at all, I'm certainly shocked because this is the biggest award I have ever won in my career," he said.
"The secret to my success is to be disciplined in my training. I'll continue to focus on competing in this year's Malaysia Super League."
The win has resonated with football supporters and other Malaysians back home in the South East Asian nation.
"Faiz is now a world icon thanks to his ability," said Penang Football Association Team Manager Zairil Khir Johari.
"It's an amazing and well-deserved achievement, not only for Faiz but for football in Malaysia as a whole," he said.
He added: "I am confident he will now inspire a whole generation of footballers in our country."
Other Malaysians began expressing joy and pride for their "national hero" and shared congratulations for his achievements.
"Without or without our votes he deserved to win and did us proud," wrote Hafiq Hasan Basri from Kuala Lumpur.
Saegaran Kana remembered the moment as "an astounding goal". "Thanks for honouring Malaysia," he added.
"Faiz has made us all proud. It is an honour to all Malaysians when the world's top football players give their respect upon an incredible home feat," said Mohd Sukhimi.
"What an incredible milestone for Malaysia. I haven't even gotten over that crazy goal yet," said Elaine Loh in a Facebook post.
Additional reporting by Woon King Chai in Kuala Lumpur.
Malaysian football star Mohd Faiz Subri has taken home Fifa's prestigious Puskas Award for the best goal of 2016, a first for his country.