It means the UK has now provided a total of £89.5 million in aid for those caught up in the Syrian civil war between forces loyal to Syrian president Bashar al-Assad and those who oppose him.
Ms Greening said: "My visit today has given me the chance to see first-hand the incredible generosity of spirit that ordinary Jordanians have shown in opening their homes to complete strangers in need.
"It is a story repeated in towns and villages in Syria's neighbours across the region, and I salute these ongoing efforts from governments and host communities alike.
"But we cannot and must not leave them to shoulder this response alone.
"This is a man-made crisis. That man is Assad."
Half of the new tranch of aid (£10 million) will be used to help Jordan deal with the influx of refugees.
According to the UN, about 6,400 Syrians have arrived at the main refugee camp in Jordan in the last 24 hours alone.
The remaining funds will be used to restock medical facilities and treat tens of thousands of injured and sick people inside Syria. It will also be used to buy vital supplies of bread and flour and winter clothing.