No. There is no specific statutory provision that obliges the employer to compensate employees for their expenses while working from home.
For example, the employer is generally not obliged to compensate the employee for his telephone, internet or power costs as well as lease or mortgage costs. Instead, the employee can set these expenses off against his tax liability. If the employee is obliged to work from home (e.g. because of an order from a public authority or the employer), he is permitted to set down a maximum of EUR 1,250 against tax (in German, Werbungskosten).
If the employer reimburses the employee's expenses on a voluntary basis, he may be obliged to list the reimbursement on the payroll (e.g. a flat-rate reimbursement for the use of internet amounting to a maximum of EUR 50 is liable for income tax of 25%, but not for a social insurance contribution).