At least one bullet hole was visible on one side of the car door and security officials were seen to be collecting evidence at the scene.
Khalid Masood, a senior police official, said Solecki "has been serving in Quetta for more than two years".
"We cannot speculate on the motive behind the crime," he told The Associated Press news agency.
There was no immediate claim of responsibility or ransom demand was reported following the abduction.
The UN confirmed that an official with the UNHCR had been kidnapped, but did not disclose the official's name or nationality, pending notification of his relatives.
Incidents of abduction have increased in Pakistan over the past year, especially in the northwest in areas on the border with Afghanistan, where several foreigners have been taken by pro-Taliban fighters.
A number of nationalist groups are fighting for autonomy in Baluchistan province, but such groups are not known for targeting foreigners.