It is the second time this season Rodgers has won the award - he also collected it back in August.
Liverpool won all five of their Premier League matches in March to put themselves firmly in the hunt for the title.
They beat Manchester United 3-0, Cardiff City 6-3, Southampton 3-0, Tottenham 4-0 and Sunderland 2-1.
Liverpool captain Gerrard and striker Suarez received the same amount of votes. Gerrard, who wins the sixth Player of the Month award of his career, scored four goals in March, whilst Suarez scored six. Suarez also won the award in December.
Rodgers said: "It's not an individual award really - all our successes are purely down to a team effort. We receive it gratefully. We've been on a wonderful run as a team and over the course of March we've had some outstanding fixtures and results.
"We are very honoured and humble to receive it. Up until now we've been performing really well and we've been working really hard. Our results are demonstrating that the improvements are taking place.
"We've got a really exciting group of young players here that are improving all the time and the senior players have been outstanding for me.
"They have really been wanting to take on board new concepts and ideas and they've been taking that on the field and performing magnificently well.
"So for us at this point our objective is still to make sure we qualify for the Champions League - that objective hasn't changed and that isn't secured yet.
"So at this moment in time the concentration is just on the performance and the next game."