Costa, 25, has scored four goals in his first three games for Chelsea since a summer switch from Atletico Madrid for a reported fee of 32 million pounds.
“I’m very happy to win this award,” Costa told Chelsea’s official website. “It is important to begin well at a new club and I’m pleased with both my start to the season and also the team’s, which is the most important thing.
“I hope to continue scoring goals to help out the team and keep making our fantastic supporters happy. I thank my teammates as they have helped me win this award.”
Swans boss Monk — who was named the club’s permanent manager this summer following a spell as interim player-manager last season — has led his side to three wins from their first three league games this term, including a opening-day 2-1 win at Manchester United.
“It’s an honour and privilege, but it’s very much a collective — it’s not about individuals,” Monk told the Swans’ official website. “For me, it’s about the players, myself, the staff around me day-to-day and the staff in the office working hard.
“We have made a great start, but that’s all it is — a start. There will be ups and downs but we will make sure that we maintain our standards and that should see us achieve a good season.”
Swansea travel to Stamford Bridge on Saturday with both sides looking to maintain their 100 percent starts to the Premier League campaign.