There were nine games in the September to October period and Strauss played in eight of those fixtures and was commended for the consistency of his performances.
He scooped the Man of the Match performance in the 18-6 victory over Connacht at the Galway Sportsground in October.
Strauss will want to carry his impressive form into the clash with the Dragons at the RDS on Friday with Leinster without a string of Irish internationals.
"I am delighted and surprised to receive this award," said Strauss.
"Obviously we have enjoyed a good run of form recently and it has been a real team effort. I would like to pay tribute to the other players and to our coaches because rugby isn't about individuals.
"I would like to thank Bank of Ireland for their sponsorship of this award, but most of all to the Leinster supporters who voted for me. I am hugely honoured by their backing.
"We are about to begin a massive period in the season and it is vital that we approach the Dragons in a positive frame of mind. They have really improved this season and we know from experience how difficult they will be.
"With so many of the players away on international duty, it will be another big test of our squad but all of the players are up for the challenge and determined to build on our previous win against Edinburgh."
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