Yes. The wrong mattress can be a reason for causing back pain. Lack of support from a mattress reinforces poor sleeping posture, strains muscles and does not help keep the spine in alignment, all of which contribute to low back pain.
Recent studies show that a medium-firm mattress greatly improves the sleep quality in people suffering from chronic lower back pain. A mattress that provides both comfort and back support helps reduce low back pain, allowing the structures in the spine to really rest and rejuvenate during the night.