Is it unusual for a 13-year-old boy to masturbate?

No: This is the time when he is entering puberty with all the hormonal changes that typically occur. During this time, there is curiosity and increased awareness of sexuality that is generally associated with masturbation and self-sexual exploration.

Pubertal: No. He is likely entering puberty and the sex hormone surges are awakening drives and desires for pleasure. If it is with a frequency that limits other activities, then should be discussed with his dr, otherwise is normal.