The 26-year-old has made more than 50 appearances in all competitions for the Red Devils this season and helped the club keep record 17 clean sheets in the league.
Smalling won the award after being voted for by his teammates and admitted it was a great privilege.
After collecting his award at the club's gala night at Old Trafford, Smalling said: "It's a massive honour to receive this from my fellow players. There are some big names on the winners' list, so it's great to add mine to it.
"It's been good that we [Blind and myself] have been able to play so consistently together and learn each other's game. We've been quite solid as a team defensively.
"[The captaincy] is a huge honour and it's great that the manager has shown faith in me. It's nice that after Michael Carrick and Wayne Rooney I get the chance. It really adds to your own sense of leadership.
"It's nice to win this award tonight, but I'm looking forward to hopefully picking up another trophy at Wembley in a few weeks."