It works as easy as the following:
ShowWindow(MdiChild1.Handle, SW_HIDE);
In previous VCL and/or Windows versions, this caused problems as the following (dated) text shows. Thanks to Yaroslav Pasichnyk for pointing out that this document was outdated.
Old Text -no longer valid
Steve Teixeira says:
You can't hide MDI children.
Windows does weird things when you try to hide
MDI children, so VCL doesn't permit it.