O'Neill, St. Louis' 26-year-old left fielder, hit safely in all six games last week, drove in at least one run in five of them and swatted three home runs, two of which came in the eighth inning and put the Cardinals in the lead.
The Cardinals have won eight straight games overall to take hold of the No. 2 National League Wild Card spot.
O'Neill finished the week with a .391 average, 10 RBIs, nine runs scored and a 1.308 OPS to win Player of the Week honors for the first time.
This is the fourth career Player of the Week Award for Ramírez, who went 10-for-20 with two homers, two doubles, seven RBIs, 10 runs scored and a 1.460 OPS over six games for the Indians.