Ovechkin had seven goals and two assists over Washington's four-game winning streak last week, as well as scoring the only shootout goal in a 2-1 win Thursday over the New York Islanders.
His scoring run included three goals, including the game winner, in a 4-3 win over Florida on Saturday. It was the 12th hat trick of Ovechkin's career.
Ovechkin is tied for first in the league with 25 goals, and ranks sixth with 43 points.
St. Louis goaltender Brian Elliott was named second star. Elliott posted a 3-0-0 record, 1.45 goals-against average and .952 save percentage in three appearances last week. He capped the week by making 28 saves for the 19th shutout of his career in a 1-0 win over Detroit on Sunday.
New York Rangers goaltender Henrik Lundqvist took third-star honours. Lundqvist started all four games for the Rangers, posting a 3-0-1 record with a 1.22 goals-against average and .962 save percentage.