Use set_item_disabled(<item_id>, <bool>)
. Here's an example:
extends PopupMenu
func _ready():
# add three items to the PopupMenu
add_item("Test1") # id: 0
add_item("Test2") # id: 1
add_item("Test3") # id: 2
# disable only the second item,
# the rest will be enabled by default
set_item_disabled(1, true)
popup() # show the PopupMenu