The dictionaries I have seen claim "ἰάομαι" can mean physical or spiritual healing.
I am assuming you don't mind conjugations of ἰάομαι.
The First Epistle of Peter uses it in a way that seems to necessitate a spiritual meaning:
when He was reviled, did not revile in return; when He suffered, He did not threaten, but committed Himself to Him who judges righteously; who Himself bore our sins in His own body on the tree, that we, having died to sins, might live for righteousness—by whose stripes you were healed. (1 Peter 2:23-24, NKJV)
John quotes Isaiah,
He has blinded their eyes and hardened their hearts,
Lest they should see with their eyes,
Lest they should understand with their hearts and turn,
So that I should heal them
John 12:40, NKJV
Are the brokenhearted in need of spiritual or physical healing? Luke records Christ quoting Isaiah:
The Spirit of the Lord is upon Me,
Because He has anointed Me
To preach the gospel to the poor;
He has sent Me to heal the brokenhearted,
To proclaim liberty to the captives
And recovery of sight to the blind,
Luke 4:18, NKJV
The Epistle of James uses it in a way that is ambiguous but, at least in some Christian traditions, includes a spiritual healing.
And the prayer of faith will save the sick, and the Lord will raise him up. And if he has committed sins, he will be forgiven. Confess your trespasses to one another, and pray for one another, that you may be healed. The effective, fervent prayer of a righteous man avails much. (James 5:15-16, NKJV)
Depending on how you interpret demonic possession and whether or not the removal of the demon constitutes physical or spiritual healing, Matthew recorded
And behold, a woman of Canaan came from that region and cried out to Him, saying, "Have mercy on me, O Lord, Son of David! My daughter is severely demon-possessed." ... Then Jesus answered and said to her, "O woman, great is your faith! Let it be to you as you desire." And her daughter was healed from that very hour. (Matthew 15:22,28, NKJV)