Compare Isaiah 53:4 with Matthew 8:16-17. You will see physical healing is in this passage, because Isaiah is quoted in Matthew to confirm prophecy (which is about healing of the sick). People often say the context of Isaiah 53 doesn't allow for physical healing but only spiritual healing (such that we were dead but are now made alive), however in Matthew 8:16-17 we have Isaiah 53:4 being quoted on the topic of physical healing.
Isaiah 53:4 King James Version (KJV)
4 Surely he hath borne our griefs, and carried our sorrows: yet we did esteem him stricken, smitten of God, and afflicted.
Matthew 8:16-17 King James Version (KJV)
16 When the even was come, they brought unto him many that were possessed with devils: and he cast out the spirits with his word, and healed all that were sick:
17 That it might be fulfilled which was spoken by Esaias the prophet, saying, Himself took our infirmities, and bare our sicknesses.