Hip-hop artist Sean, Bollywood actress Shetty and world light welterweight boxing champion Khan said a key outlet for South Asian talent would be "tragically lost" if the station closed down.
They were among 158 public figures who made the plea in a joint letter to The Guardian newspaper.
"We are writing to express our profound shock at the BBC director general Mark Thompson's proposals to close down the BBC Asian Network as a national station, " the signatories said.
"The BBC we have grown up with has always prided itself on celebrating diversity.
"In that respect the Asian Network is a national platform for musicians, Asian culture in general, news, debate and documentaries.
"It provides a key platform for the national Asian community, and offers an outlet to Asian talent, which is demonstrably underrepresented in the more mainstream BBC. This would all be tragically lost if these proposals are agreed.
"We urge the BBC Trust to reconsider this proposal and stop the closure of a valued station which is greatly needed by your licence-fee-paying audience nationally.
"As loyal licence-fee payers, we trust we will not be let down."
Other signatories included Lord Karan Bilimoria, the founder and chairman of Cobra Beer; England one-day international cricketer Vikram Solanki; Bend It Like Beckham film director Gurinder Chadha; musicians Asian Dub Foundation, Jazzie B and Apache Indian; comedians Sanjeev Bhaskar and Shazia Mirza; and writer Meera Syal.
Several parliamentarians, trade union leaders and musicians were also among the signatories.
The British Broadcasting Corporation said Tuesday it would close the Asian Network and 6 Music radio stations from next year and slash spending on its online services.
The shake-up came after criticism of its market dominance. The changes, in a report entitled Putting Quality First are to free up an extra 600 million pounds (890 million dollars, 660 million euros) to be spent on programme-making.