The Swansea boss was named the Premier League's most impressive so far this season in a poll conducted by the managers' union, winning almost half the votes.
Laudrup has built on Brendan Rodgers' work in south Wales, establishing City in the top half of the league and delivering the Capital One Cup in his first nine months at the club.
He told the club website: "It's always an honour to receive recognition, but I always consider them more important when they come from your colleagues.
"I felt the same as a player and that hasn't changed now that I'm a manager.
"It's something special coming from your colleagues because they are the ones you are competing with on a weekly basis on and off the pitch."
Laudrup's bargain £2m signing Michu was voted best new recruit in the LMA survey, while Liverpool winger Raheem Sterling was named best young player.