Yes, hypochondria (also known as health anxiety and illness anxiety disorder) can cause anxiety. When you are worried that you may have a serious medical illness, and the doctors and lab tests can't find anything wrong, then this makes you worry that the doctors and the tests are missing the diagnosis that you are certain that you have. So this belief that you have a serious medical illness, combined with the negative findings from the doctors and the medical tests, makes you anxious and worried.
Although hypochondria is classified as a somatic disorder, it is more suited to the classification of an anxiety disorder, as the negative thoughts and beliefs lead to anxiety, and the anxiety makes you behave in ways that maintain the negative, vicious cycle of hypochondria:
