Some members of the trade union UNITE said the strike is expected to significantly affect operations at Foyle Port.
The union said the dispute centres on a rejected demand for a 2.1% pay rise this year, following a pay freeze.
Foyle Port said average remuneration for employees last year was 58% above the median annual earnings for the local council area.
Unite said that almost every worker at the port and their families were "struggling to make ends meet and now face a second year of poverty pay".
Foyle Port said the Unite statement "does not accurately reflect the context of the ongoing dispute with a minority of employees at Foyle Port".
The spokesperson added that they "wholly reject the loaded term 'poverty pay', as referenced in the union's statement" and said they have "consistently paid inflationary rises over many years".
On Monday morning, between 25 and 30 Unite members were at a picket line at the port.
BBC News has further coverage of the dispute.
