The Daily Monster Egg can be found in the Shop. It costs 
10 and can only be bought once every 24 hours. Meaning that once it is bought, you may only buy it 24 hours after the time of purchase.
The egg comes with a 70%, 25%, 4% and 1% chance of monsters being hatched. The higher you level up, the more valuable the egg becomes, as after level 301, there is a 1% of receiving an Infinite.
For more information on what monsters appear in what egg at each level, visit Egg Levels.