The Gunners saw plenty of the ball in the first half, but they could not breach the Potters' defence.
Jonathan Walters thought that he had broken the deadlock midway through the first half, but he was denied by the linesman's flag.
Arsene Wenger's men continued to dominate possession in the second half, but struggled to create any real opportunities.
The best chance of the match fell to Abou Diaby, who could not get the ball from under his feet and stabbed a right-footed shot wide from inside the area.
Olivier Giroud nearly scored what would have been an unbelievable effort in the 85th minute.
The Frenchman spotted Asmir Begovic slightly off his line and attempted to float the ball into the net from all of 30 yards out.
In the end, Stoke managed to hold on and claim a point.