A new report from the charity was published ahead of the World Economic Forum in Davos - a week-long meeting of the global elite, with three of the 26 richest people set to attend.
The report found that billionaires around the world saw their combined fortunes grow by $2.5 billion (2.2 billion euros) each day in 2018, an annual increase of 12 percent, and urged governments to slap more taxes on the wealthy.
The world's richest man, Amazon CEO Jeff Bezos, saw his fortune increase to $112 billion last year, Oxfam said, pointing out that just one percent of his wealth was the equivalent to the entire health budget of Ethiopia, a country of 105 million people.
"Oxfam is saying in this report with evidence that extreme inequality is out of control," Byanyima said.
The 3.8 billion people at the bottom of the scale meanwhile saw their relative wealth decline by $500 million each day, or 11 percent last year, Oxfam said, stressing that the growing gap between rich and poor was undermining the fight against poverty, damaging economies and fuelling public anger.
"Citizens are angry and frustrated," Byanyima said.
"They are seeing themselves working really hard, but they are seeing that... the things that they expect, a good education for their children, health when they fall ill, social protection when they get older... aren't there for them."
At the same time, she said, "they are seeing a few people running away with wealth and without paying their fair share."
The numbers are stark: Between 1980 and 2016, the poorest half of humanity pocketed just 12 cents on each dollar of global income growth, compared with the 27 cents captured by the top one percent, the report found.
Oxfam warned that governments were exacerbating inequality by underfunding public services like healthcare and education at the same time as they consistently under-tax the wealthy.
Calls for hiking taxes on the wealthy have multiplied amid growing popular outrage in a number of countries over swelling inequality. In the United States, new congresswoman Alexandria Ocasio-Cortez made headlines earlier this month by proposing to tax the ultra-rich up to 70 percent.