There are two parts of the game that have a time limit of sorts - you won't "fail" a mission by taking too long but there are lasting effects if you take too long to complete the mission objectives. In order, these are as follows;
At Sarif HQ, after the prologue
After the prologue, once you've arrived back at Sarif HQ post augmentation, you will be told to meet David Sarif at the helipad to start the first mission, while commenting that you need to go and meet up with Pritchard to get your retinal prosthesis recalibrated.
If you spend more than 15 minutes looking around, the hostages in the next mission will be dead on arrival. David will warn you once you reach about half way through the available time limit.
Later in the game upon returning to Hengsha for the second time, Malik's flight will be shot out of the sky (with you on board). You will start in a level under siege with multiple waves of enemies attacking consisting mainly of ground soldiers at first before escalating to security robots. If you take longer than 10 minutes to clear all of the hostiles (shortly after the security robots are activated), Malik's ship will be destroyed, along with Malik.