on monday morning是正确的。on用法：表示“在物体的表面上”，只能用on的表达方式有onthe next morning，onthe following。
morning例句
1.What time do you usually wake up in the morning?
通常你早晨几点钟醒？
2.You may stay until morning,if you wish.
如果你愿意，你可以一直待到早晨。
3.I want to make an early start in the morning.
我想早上早点出发。
4.The system was down all morning.
系统整个上午都无法运行。
5.What time do you leave the house in the morning?
你早晨几点出门去上班？