Hotels and small shops in Makkah offer laundry services; in Mina there are virtually none, so pack enough changes and consider hand-washing with unscented soap.
Laundry services are available in Makkah through several channels: most hotels offer laundry services (though they can be expensive during peak season), there are small laundry shops in the streets around the Haram district, and some areas have self-service laundromats. Turnaround time varies from same-day to 24 hours depending on the season's demand.
During the days of Hajj in Mina, laundry facilities are essentially nonexistent, so plan to bring enough clothing changes for those days. Ihram garments can be washed and reused — there is no religious prohibition on washing them, but use unscented soap while in the state of ihram. Many pilgrims bring travel-size detergent packets and wash small items by hand in their hotel room sink. Pack quick-dry fabrics to make this easier.