The learning process itself does not cause stress if it is approached with a relaxed but focused mindset. A closed mind will experience all the learning stress in the world and still not learn much.
The three main factors of learning are goals, mindsets and distractions.
Having proper goals is important because learning useless stuff is... well... useless. If you can't separate wheat from chaff, you will be placing yourself under stress for no good reason. Define your goal clearly and make a sensible study plan.
The proper mindset is what determines whether studying will result in learning. The nastiest error people make is to think they already know something well, and they refuse to correct or improve that 'knowledge'. If you are not ready to let go of old falsehoods, learning becomes a very difficult and very stressful process.
If your line of thought is constantly interrupted with distractions, losing and establishing focus again is mentally very demanding. Jumping from one state of mind to another against your will is a prime source of stress.
Keep your mind clear and flexible. Don't cling to knowledge or understanding, and you will be able to keep learning stress to a minimum.