It looks like you asked a similar question on Quora.
As mentioned there, the ERD is simply a mapping of the data you intend to store and the relations amongst that data.
You can still make an ERD with MongoDB as you still want to track the data and the relations. The big difference is that MongoDB has no joins, so when you translate the ERD into an actual schema you'll have to make some specific decisions about implement the relationships.
In particular, you'll need to make the "embed vs. reference" decision when deciding how this data will actually be stored. Relations are still allowed, just not enforced. Many of the wrappers for MongoDB actually provide lookups across collections to abstract some of this complexity.
Even though MongoDB does not enforce a schema, it's not recommended to proceed completely at random. Modeling the data you expect to have in the system is still a really good idea and that's what the ERD provides you.
So I guess the equivalent to the ERD is the ERD?