The low prices the US entrepreneur is quoting for his new Falcon 9 vehicle mean it is winning contracts that in the past would have gone to Ariane. Mr Musk said that the cost of producing the current European rocket would kill it as a commercial entity.
"Ariane 5 has no chance," he told BBC News.
"I don't say that with a sense of bravado but there's really no way for that vehicle to compete with Falcon 9 and Falcon Heavy. If I were in the position of Ariane, I would really push for an Ariane 6." Ariane's future will be a key topic this week for European Space Agency (Esa) member states.
They are meeting in Naples to determine the scope and funding of the organisation's projects in the next few years, and the status of their big rocket will be central to those discussions.
Although its great reliability has helped Ariane achieve a level of dominance in the global market for the launch of large telecommunications satellites, the rocket still requires subsidy from Esa nations. Support payments totalling 217m euros have been agreed for the years 2011 and 2012.
SpaceX's Falcon is a new entrant to the launcher market. It has so far made only four flights, but it has a backlog already of more than 40 contracted launches. Its quoted price under $60m per flight is proving highly attractive to satellite operators who have to pay substantially more to get on an Ariane.
"Not only can we sustain the prices, but the next version of Falcon 9 is actually able to go to a lower price," warned Mr Musk.
"So if Ariane can't compete with the current Falcon 9, it sure as hell can't compete with the next one."
The SpaceX CEO and chief designer was speaking at the Royal Aeronautical Society where he was being awarded a gold medal for his work to advance the commercialisation of space.
Esa member states recognise that aggressive competition from the likes of SpaceX demands Europe reduce the cost of the Ariane product, but there is deadlock over how that should be achieved.