The Kurdish offensive is supported by US-led coalition air strikes.
Meanwhile, the Iraqi army says it has launched an offensive to recapture the western city of Ramadi from IS.
The army press office said the offensive was under way "along the northern, western and south-western axes, with air support", official Al-Iraqiyah TV reports.
`They stole our dignity`
Witnesses said the Kurdish fighters, some carrying rocket-propelled grenades, moved into Sinjar on foot.
A hospital, several public buildings, a silo and cement factory have all been secured, the Kurdistan Regional Security Council (KRSC) said in another tweet.
The offensive to retake Sinjar began in earnest at dawn on Thursday, with some 7,500 Peshmerga fighters closing in on three fronts after coalition warplanes bombed IS positions, command-and-control facilities and weapons stores.
Within hours, they had successfully blocked Highway 47, the main road between Mosul, to the east, and Raqqa to the west, and secured three surrounding villages.
The Kurds estimated that there were almost 600 IS militants in Sinjar before the offensive began, but the coalition said they believed some 60 to 70 had been killed in Thursday`s air strikes.
Thousands of Yazidis who fled the Sinjar area when it fell to IS in August 2014 are reportedly taking part in the offensive.
Turkish Kurdistan Workers` Party (PKK) rebels have trained a Yazidi militia, while others have joined the Peshmerga.
Hussein Derbo, the head of a Peshmerga battalion made up of 440 Yazidis, told the Reuters news agency: "It is our land and our honour. They [IS] stole our dignity. We want to get it back."
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