Koscielny limped off after just four minutes at Goodison Park and Gunners boss Arsene Wenger said afterwards he expected the centre-back to be out for three weeks.
"He has a groin strain. That's usually three weeks," said Wenger.
Wenger was pleased to leave Merseyside with a point despite his side dominating the last 10 league meetings with Everton, winning eight and drawing just two.
"It was a game of big physical intensity, we had a good start and after that I felt Everton came back into it and their direct game was always a threat," he said.
"There are regrets on the goal we conceded but 1-1 is a fair result and it is a good point here.
"We needed to show great spirit to get away with a point and I am pleased with the effort they put into the game."