Edited: This post is old now and the information is incorrect
Currently the money tree can not be harvested, sims can only sell directly from the money tree itself. Maybe a bug, but probably by design.
If you need a money tree 'seed' to complete your plant collection then you can wait until the Money Tree is ready for harvesting and then place the tree into your sims Household Inventory. This will place the tree and it's harvestables into the inventory separately, so then drag out the fruit and now you will have around 5 money tree fruits. If the fruit still hasn't registered by this stage drag it into your sims personal inventory.
For some reason when you purchase the Money Tree from the Reward Store the fruit doesn't always register in your sims collections tab - this way it will.
This is also a bit of an exploit as this way you could have multiple Money Trees after only spending the satisfaction points to buy one. (I just left the extra fruit in my game in my sims household inventory as I get bored very quickly if my sims become too wealthy too quickly!)
Also note once you've placed the Money Tree in your sims Household Inventory the fruit becomes harvestable after that just like any other plant. (As opposed to only be able to sell directly from the tree like I stated above.)