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Police were called to reports of a distressed man in the Medway City Estate area.
Several officers were seen running after in a field off Berwick Way.
It happened at around 5.30pm, just before the Anthony's Way roundabout, and four police vehicles were involved.
Three police cars were abandoned by officers at the roundabout as they continued the pursuit.
A police spokesman said they had been dealing with "a distressed man".
"Officers attended and following an area search detained the man in an area of land off Berwick Way," he said.
"He has since been handed into the care of medical professionals."