It is the second consecutive player of the week honor for Davis, who ended the regular season last year sharing the honor with Tigers right-hander Justin Verlander on Oct.1.
The last Oriole to win the award in back-to-back weeks was Eddie Murray on Sept. 13 and Sept. 20, 1981.
Davis entered Monday's game in Boston leading the major leagues in OPS (1.636), slugging percentage (1.136) and RBIs (17). He was also second in total bases (25) and sixth in batting average (.455).
Davis was 0-for-2 with two walks in Monday's 3-1 loss to the Red Sox.
He set a major league record with 16 RBIs through the season's first four games, breaking the previous mark of 12. He also became just the fourth player to homer in the first four games of the season, joining Willie Mays (1971), Mark McGwire (1998) and Nelson Cruz (2011).
After Friday's game-winning grand slam in the Orioles' home opener win over the Minnesota Twins, Davis had 11 homers in his past 11 regular-season games dating back to last season.
Davis also became the first major leaguer to hit a homer and record at least three RBIs in the first four games of the season since the New York Yankees' Bill Dickey accomplished the feat in 1937.
Tampa Bay Rays manager Joe Maddon, whose team Davis recorded three homers and 11 RBIs against last week, said Davis should just receive the AL Player of the Month award for April right now.
“[He] should be player of the month, because there is nothing anybody else can accumulate in the next couple of weeks that's going to surpass what he did in the first week," Maddon told the Tampa Bay Times. "Just give him the whole month.”
Davis was selected over former Orioles first baseman Mark Reynolds of the Cleveland Indians — who had four homers and seven RBIs — Seattle Mariners first baseman/outfielder Mike Morse, Boston third baseman Will Middlebrooks, Boston left-hander Jon Lester and Texas Rangers right-hander Yu Darvish.