Dynamically partitioning a table from main to remote mySQL server

I have a table in my DB which I need to partitionate based on a foreign key attribute. So the number of partitioned tables is the same as the number of different values present for the foreign key.

EDIT: I have replication setp up, where a table in the master is replicated in four slave servers. The slaves do not need to replicate the WHOLE table in the master server but only a partition of it as shown in the figure. How can achieve this?

Image: Replicating partitions