About 100,000 workers are expected to vote on the strike, which would affect about 130,000 Verdi members at Deutsche Post. The strike would not affect about 53,000 civil servants who also work for the postal service.
Voting will continue until Tuesday. Verdi said it will announce results on Wednesday for walkouts that could begin on May 2.
The trade union and Deutsche Post were unable to agree over the weekend on wages, shifts and layoff protection.
The Post is offering layoff protection through June 30, 2011 and a pay raise of about 5.5 percent over the next two years. But the company wants workers to work 41 hours a week instead of 38.5 hours, something Verdi says could endanger 12,500 jobs.
The union also wants to see wages increased 7 percent over the next 12 months.
A series of limited strikes at mail sorting centres, starting on Sunday night, left tonnes of letters and bulk mail undelivered across Germany this week.