It can be argued that with to tell, which is normally a bitransitive verb taking both sorts of objects as in to tell someone something, can exist with just an indirect object alone.
There is an unspoken “something” that is being alluded to here, and that thing unsaid is the direct object, with the person receiving the information being in the indirect object position.
However, this analysis is not universally accepted. Others view this particular situation as one where the indirect object has passed to a direct one. The OED seems to be one of these; the following citation is taken from its entry for the verb tell:
trans. to tell a person (the originally indirect or dative personal object becoming the direct).
Note the parenthetical portion. They have stopped calling it an indirect object there. It’s the only object in sight, so it “must” be a direct one. I guess.
In other languages that have stronger case systems, this sort of use can take an indirect object by itself, and when it does, it is still marked in the dative’s indirect object case. So for example, the Spanish for tell me it is dímelo; if you wanted to add and tell her too while you’re at it, you would have to say dile to mean “tell her” using the dative enclitic pronoun le. You cannot use the accusative enclitic pronoun la, because it is still indirect. So they in Spanish do not reanalyse the remaining object as a direct one. It stays dative in their minds. It is that line of reasoning that leaves it as an indirect object for some English grammarians, too.
Now, you can construct that same situation in English, but to do so you have to go back to when English was what for us today was a foreign language. A thousand years ago when English had a more robust case system, you sometimes had certain verbs that took only a dative case pronoun for their complement without an accusative case one to go along with it. So one could (perhaps) say they only took an indirect object. However, most of the time we translate those uses from Old English and dative objects into regular direct objects today so as not to confuse people.
However, one rare place where that still occurs is in the frozen relic verbs meseem and methink, once spelled me seems and me thinks (or me thought and so on). There the Old English dative me, which in those expressions came before the actual verb, became stuck when it fossilized. We no longer think of it as being an indirect object. But it really is an isolated dative, because it is the very sort of “to/for me” kind of “dative of interest” you find in modern expressions like cry me a river or sing me a song. So meseems just means it seems to me. That’s why the singular is meseems, as in Meseems unlikely that he shall pursue us meaning it seems unlikely to me.
But those are just curiosities from the museum case, not productive uses. If you abbreviate sing me a song to sing me, folks are going to think that use of me has switched to a direct object use from an indirect object one, and wonder what it is you really meant by that.
Best Answer
It's untrue that the verb is necessarily intransitive. You can walk down the street, but you can also walk the dog. All it means is that the verb is being used in an intransitive fashion.
Idiomatically, we rarely put a prepositional phrase between the verb and the direct object. We can show to the door an uninvited guest, but it's more common to do the other way around.
Of course, many individual prepositions become attached to verbs (sit down, walk around, show up) and often that preposition-like particle (not a phrase, just a single word) is left next to its verb. Do you throw up your lunch or throw your lunch up? Do you beat down the grass or beat it down? Piss off your spouse or piss it off?
(Funny how you always put the particle after the object, if the object is a pronoun. You almost never "throw up it" or "piss off her". Funny language, English.)