Chief Muktar Otieno was seized early on Thursday morning on the road to Mandera town, close to the border between Kenya and Somalia.
Assistant chief Abdinoor Dakane told the BBC that Mr Otieno was tied to a tree and shot dead by the militants, after locals failed to pay a ransom.
Al-Shabab has staged a series of attacks in Kenya in recent years.
Kenyan troops are part of the African Union mission battling the Islamist militants in Somalia.
Al-Shabab has not yet commented on Mr Otieno's killing.
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Kenya failings drive al-Shabab recruitment
Who are Somalia's al-Shabab?
Meanwhile, Kenya has extended an amnesty for al-Shabab militants to hand themselves in by a further 14 days.
When making the announcement, Interior Minister Joseph Nkaissery said some people had already taken advantage of the amnesty but declined to say how many.
Mr Otieno was abducted happened 10 km (five miles) from the place where al-Shabab gunmen killed 28 people travelling on a bus in Mandera county last November.
According to the assistant chief, who witnessed Mr Otieno's abduction, a group of local elders managed to track down the assailants to a town on the Kenyan-Somali border.
The group pleaded with the militants to release the chief, but when they failed to pay a ransom of 4m Kenyan shillings ($42,000; Â£28,000), Mr Otieno was shot dead in front of the clan elders, he told the BBC Somali service.
Mr Dakane told the BBC that he was now resigning from his position as assistant chief of Arabia ward because he feared for his life.
There has been no official comment yet from the Kenyan authorities.
The killing comes at a time of heightened tension over security in Kenya, after Islamist al-Shabab fighters killed 148 people, mainly students, during an attack on a university in Garissa earlier this month.

The Brit Award winner and three-time Mercury Music Prize nominee tops the bill at the 13th annual festival at Glanusk Park, Powys, on 20 August.
Fellow UK acts Belle and Sebastian, on Thursday, James Blake, on Friday, and Wild Beasts, on Sunday, have already been named as the other headliners.
The festival was a sellout last year, with about 20,000 people attending.
Festival director Fiona Stewart said: "Laura returns for her third performance at Green Man, her legendary performances have always gone down a storm and we're already feeling awestruck imagining her Saturday night set, full of new album material."
Other new acts booked for this year's Green Man festival include Charlotte Church's Late Night Pop Dungeon - "a karaoke experience unlike any other you've experienced before, or ever will again", re-formed 1990s alt-rockers Lush, and DJ Pete Paphides.
Among the other prominent acts appearing are Grandaddy, Tindersticks, White Denim, Fat White Family, Cate Le Bon, Gun Outfit, and The Membranes.
Previous headliners have included legendary Belfast-born blues and rock singer Van Morrison, ex-Led Zeppelin frontman Robert Plant, US singer-songwriter Patti Smith, Cardiff rockers Super Furry Animals, Fleet Foxes, Jarvis Cocker and Doves.
Founded in 2003, Green Man has become one of the most popular alternative festivals.
It won the 2010 best medium-sized event and 2012 best "grass roots" event at the UK Festival Awards, and 2015 best festival at the Live Music Business awards.
Suspected al-Shabab militants have abducted and killed a traditional chief in northern Kenya, a local elder says.
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Alt-folk singer-songwriter Laura Marling has been unveiled as a headline act for the 2016 Green Man festival.