Launched at the Consumer Electronics Show in Las Vegas, the Qualcomm Tricorder X Prize will involve entrants developing a portable tool capable of capturing "key health metrics" and diagnosing a set of 15 diseases.
The device must not be heavier than 5lb (2.2kg), enabling it to be carried in a similar way as Dr McCoy did on the science fiction TV series.
On Star Trek, which was first broadcast in 1966, the doctor was able to use the tricorder to diagnose an illness by scanning someone's body.
Technology firm Qualcomm said that the prize would "stimulate innovation and integration of precision diagnostic technologies, making reliable health diagnoses available directly to 'health consumers' in their homes".
It added: "The dire need for improvements in health and healthcare in the US has captured the attention of government, industry, and private citizens for years. But a viable solution has yet evaded one of the most technologically advanced, educated and prosperous nations on the globe.
"Integrated diagnostic technology, once available on a consumer mobile device that is easy to use, will allow individuals to incorporate health knowledge and decision-making into their daily lives."
Organisers said that entrants are free to stipulate any features on the device, including touchscreens or sensors, but they must provide capacity for people to store and share their medical information over the internet.
Previous X Prize winners have gone on to influence real world technology, including the 2004 Ansari X Prize awarded to a privately-funded reusable spacecraft made by the SpaceShipOne team.
Many of the breakthroughs were later utilised by Sir Richard Branson's Virgin Galactic initiative.
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Discussing the latest X Prize challenge, Imperial College London's professor Jeremy Nicholson said that there were already medical devices that could diagnose illness.
However, the head of department surgery at the university told BBC News that creating a lightweight tricorder-style product would be difficult.
"The most likely sort of technology would be something that detects metabolites," he said.
"What we use in our laboratory is big - the size of a Mini. The challenge is sticking it all into one device."
He added: "The challenges are: What is it you detect, what are the samples you can get and how do you put it all together in one gizmo?
"I don't think there'll be many people getting that prize in the near future."
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