We are thinking of using a REST interface for communication between internal apps. App A will have to pass a fair bit of data representing a financial portfolio to app B.
No, it's pretty much up to the server implementation if there's any such limit.
There's a limit on the size of a URL (if you wish to put large amounts of data on the URL, like with a GET), but no defined limit for a POST or PUT.
As Will Hartung said, there is no limit in the standard (RFC 2616). But every implementation has its own limits. A few examples:
These implementation limits are usually just the default configuration values, and can be changed to larger ones if required.