Company spokesman Rich Young says it sought the injunction after incidents of sabotage, harassment and obstruction at its facilities.
The injunction limits picketing by members of the International Brotherhood of Electrical Workers.
Verizon obtained similar injunctions in New York, Pennsylvania and Delaware.
Verizon also filed unfair labor practice charges Friday against the IBEW and the Communications Workers of America, claiming they haven't bargained in good faith.
A spokeswoman for IBEW Local 827 in East Windsor declined comment. An after-hours message left for a CWA spokesman was not returned.
About 45,000 Verizon landline workers from Massachusetts to Virginia went on strike Sunday, protesting demands for contract givebacks.