Is it normal for stitches to itch after a week?

Itchy stitches. Yes. When wounds heal it ' not unusual for them to itch w/ or w/out sutures. Importantly you should rule out other causes for itching: topical antibiotic/tape or suture allergic reaction, wound infection, superinfection w/ yeast or other organisms. As long as the wound is not draining, red, hot or swollen ; you dont have a fever or feel ill, it is probably normal. Call your doc if concerned.