The Messenger of Allah ﷺ had himself cupped when he was fasting and wearing ihram (pilgrim garb). (Using translation from Abū Dāʾūd 2373)

أَنَّ رَسُولَ اللهِ ﷺ احْتَجَمَ وَهُوَ مُحْرِمٌ صَائِمٌ