MyBB Community Forums

Is there any feature to do this? I would like to suspend a user for 1 week and he can not upload an avatar (Stays default avatar)

in default MyBB,
if the account is banned or temporarily suspended then user does not have access to user control panel
so such suspended users do not have access to avatar settings. earlier chosen avatar is retained.

banned users' avatar doesn't change automatically to the default avatar of your forum.
a custom plugin might be required for such purpose.

A custom plugin is a good option.
Another option is to use Group Promotion. What you can do is -
1. Duplicate an existing usergroup
2. Remove avatar permission from the duplicate usergroup
3. Add a group promotion that a user gets promoted to this usergroup after a week.
4. Move the user to the duplicate usergroup
(NOTE: I have not tried it but I thought of it just now and hopefully should work.)

Hope it helps.
WallBB