Hamas security forces quickly dispersed the gatherings.
Hundreds joined marches in Gaza City, the southern town of Khan Younis and other locations, chanting "what a shame" and in one place burning Hamas flags, before police moved in and broke up the protests.
Police destroyed mobile phones of people who were filming in Khan Younis, and witnesses said there were several arrests.
Young supporters and opponents of Hamas briefly faced off, throwing stones at one another.
The demonstrations were organised by an online movement called "alvirus alsakher," or "the mocking virus".
It was not immediately known who is behind the movement.
Hamas rules Gaza with an iron fist, barring most demonstrations and quickly stamping out public displays of dissent.
The Islamic militant group seized control of Gaza in 2007 from the forces of Palestinian President Mahmoud Abbas, prompting Israel and Egypt to impose a crippling blockade on the territory.
Israel says the closure is needed to prevent Hamas, which does not recognise Israel's right to exist, from building up its military capabilities.
The closure has devastated Gaza's economy, sent unemployment skyrocketing and led to frequent power outages.
During the current heat wave, people have been receiving four to six hours of power a day due to heavy demand.
"Where is the electricity and where is the petrol?," the crowds shouted in Khan Younis.
"What a shame. What a shame."
Protesters also criticised Hamas for deducting a roughly $US15 ($A23) fee from monthly $US100 stipends given to Gaza's poorest families by the wealthy Gulf state of Qatar.
There was no immediate comment from the Hamas authorities.
