Her Lumos Foundation is raising money to provide food, hygiene and medical kits to those impacted by the crisis.
The money raised will support their evacuation from the country, as well as supporting families, foster carers and providing psychological support to children.
The Harry Potter author, 56, tweeted: “I will personally match donations to this appeal, up to £1m.
“Thank you so, so much to all who’ve already donated, you’re enabling @lumos to do crucial work for some of the most vulnerable children in Ukraine.”
Lumos, which was co-founded by Rowling in 2005, has been working with the Ukrainian government to better protect vulnerable children and reform its care system.
A message on its website warned the Russian invasion “means more children are now in danger”.
The charity has been operating in the Zhytomyr region of Ukraine, which lies to the west of the capital Kyiv.
It estimates there are more than 1,500 children trapped in orphanages there, with thousands more at risk of family separation and displacement.
Speaking on BBC Newshour, Irina Malanciuc, director of programmes for the charity, said: “Children in institutions, in care, are one of the most vulnerable groups and this is a vulnerable group who need to be supported.”
On Monday, Russian military forces opened fire on the city of Mykolaiv, 480 kilometres south of Kyiv, according to Ukraine’s General Staff.
Rescuers said they were putting out fires in residential areas caused by rocket attacks.
Shelling also continued in the suburbs of Kyiv which has been cut off from electricity, water and heating for three days.
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