Lugansk is the main city of one of the two rebel- controlled areas in eastern Ukraine where violence has been uninterrupted since a pro-Russian separatist uprising in spring 2014.
The first explosion occurred around 12:30 GMT in the city centre, said Alina Zhivolup, spokeswoman for the communications ministry of the self-proclaimed Lugansk People's Republic.
"One woman died and five people were wounded and taken to hospital," she said.
A second blast "from an explosive device" went off nearby about an hour later, she added, injuring two more people.
The conflict between the separatists and Kiev forces has already killed over 10,000 people and clashes continue across the frontline despite a number of ceasefires.
Kiev and the West accuse Russia of stirring up the conflict and sending troops and weaponry across the border.
Moscow denies the accusations, saying only that off-duty soldiers and volunteers have gone to fight in Ukraine.
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