An official in the electoral commission confirmed the death of a colleague in the incident.
Sheikhi said the aircraft managed to land safely at Benina International Airport, which serves the eastern city of Benghazi, cradle of the 2011 rebellion that toppled Kadhafi's decades-long regime.
Ian Martin, head of the United Nations mission to Libya, urged "all voters to exercise their hard-earned democratic right to elect their National Congress representatives" while condemning the deadly attack on the helicopter.
"I call on every group and individual to refrain from violence or any actions that may intimidate voters from exercising this right, and to ensure that the election is conducted with the highest standards of mutual respect," he said in a statement.
Also on Friday, two rockets hit the Benghazi Medical Centre, without causing casualties or material damage, an official there said.
The violence came after protesters late on Thursday and on Friday targeted the country's key oil-producing region in the east of the North African desert nation.
"We have shut Al-Sedra, Haruj, Zuwaytina, Brega and Al-Hariga in protest over the distribution of seats in the (incoming) congress," protest leader Ibrahim al-Jadhran told AFP.
Jadhran said he heads the Wadi Ahmar movement which wants seats in the new General National Congress to be evenly split along regional lines.
Instead the authorities, citing demographic considerations, have given 100 seats to the western region of Tripolitania, 60 to the eastern region of Cyrenaica, and 40 to Fezzan in the south.
An oil industry expert downplayed the disruptions in the east, however, predicting it will all blow over after polling day and noting that many major oil firms had evacuated expats anyway, anticipating some unrest.
"This is just people jockeying for position," he said, requesting anonymity.
"In terms of worldwide ramifications, it is a minor disruption because it will be for a short term, until elections are over."
Jadhran said that the Wadi Ahmar group has no ties to a Benghazi-based tribal and political faction, known locally as the federalists, which has similar demands and has threatened to boycott the vote.
The move to shut down oil facilities in the east began late on Thursday with armed protesters forcing the closures of Al-Sidra, 35 kilometres (20 miles) west of Ras Lanuf, Haruj, and then heading eastward to Brega.
Earlier on Thursday, suspected arsonists ravaged a depot containing electoral material in the eastern city of Ajdabiya.
And last Sunday, armed men ransacked election offices in Benghazi.
Tareq al-Tahi, senior superintendent at Al-Sidra, said his terminal had been forced to stop production on Thursday by a group in armoured vehicles mounted with anti-aircraft guns.
"The situation is the same in Ras Lanuf, Brega, and Haruj," he said.
Groups demanding greater representation in the east are not the only concern ahead of the election.
The weeks before the election have been marred by fighting between different communities, with bloody clashes in western hilltop towns claiming more than 100 lives and fighting in Kufra in the south leaving dozens dead.
Security services have also warned that supporters of the former regime may seize the opportunity to disrupt the vote to elect a national assembly, which will be tasked with appointing a new government.
Islamist groups in the east also oppose the vote, saying the devoutly Muslim country needs no constitution other than the Koran.
Oil production is the major source of government revenues in Libya, and has reached 1.55 million barrels per day, nearing pre-war levels, officials say.
The oil complex at Ras Lanuf lies 360 kilometres (225 miles) west of Benghazi, birthplace of the revolt that ousted Kadhafi, who was captured and killed in October last year.