Last week, militants attacked a Chevron facility in the impoverished Delta where tensions have been building up since authorities issued an arrest warrant in January for a former militant leader on corruption charges.
Shell has been evacuating workers from Bonga, a union official said as local media reported an unconfirmed militant attack in the area.
"The evacuation is being done in categories of workers and cadres," Cogent Ojobor, chairman of the Warri branch of the Nupeng oil labor union, said. "My members are yet to be evacuated."
He gave no numbers.
A Shell spokesman said earlier that oil output was continuing at its oil fields in Nigeria while it was monitoring the security situation.
Vice President Yemi Osinbajo in the evening in the capital Abuja met executives from Shell, France's Total, and Italy's Agip and Chevron. All declined to talk to Reuters.
"All of us as stakeholders are concerned and we have agreed to work together to ensure that production is not disrupted," said Henry Dickson, governor of the oil-producing Bayelsa state in the Delta, who took part in the meeting.
"This is a time that we cannot afford to have any disruption, not to talk of vandalism of critical national assets," he said.
In separate violence, gunmen killed four policemen traveling to Bayelsa's capital Yenagoa, police said.
A group known as the Niger Delta Avengers has claimed responsibility for the Chevron attack. The same group has said it carried out an attack on a Shell oil pipeline in February which shut down the 250,000 barrel-a-day Forcados export terminal.
Residents in the Delta have been demanding a greater share of oil revenues. Crude oil sales account for around 70 percent of national income in Nigeria but there has not been much development in the region.
President Muhammadu Buhari has extended a multimillion-dollar amnesty signed with militants in 2009 but upset them by ending generous pipeline protection contracts.
The militancy is a further challenge for a government faced with an insurgency by the Islamist militant Boko Haram group in the northeast and violent clashes between armed nomadic herdsmen and locals over land use in various parts of the country.