The Android version of Instagram sends push notifications when a new like, comment, contact, photo of you is received. Disable and turn off Instagram notifications on your Android device, by doing as follows:
1. Open Instagram for Android
2. Go to your profile (Tap the last tab)
3. Tap the three dot icon on the top right to open Options
4. Tap Push Notification under Account settings
5. Now specify whether to turn off the entire notifications, or receive notifications from people you follow, or from everyone, for different events: Like notifications, comment notifications, Contact notifications, photos of you.