You can use the setRingerMode() method of AudioManager class. 

AudioManager audiomanage = (AudioManager)getSystemService(Context.AUDIO_SERVICE);
audiomanage.setRingerMode(AudioManager.RINGER_MODE_SILENT);

 The value that you pass to the method should be one of RINGER_MODE_NORMAL, RINGER_MODE_SILENT, or RINGER_MODE_VIBRATE

Also note that you have to add following permission to the manifest file

android.permission.MODIFY_AUDIO_SETTINGS