The 23-year-old Brighton central defender made his international debut in the 1-0 friendly win over Austria last week and backed that up in Sunday's match against the Romanians.
Alexander-Arnold was ruled out after suffering a thigh injury in the Austria match "and Southgate took his time to decide which of his standby players would come in.
White had an outstanding season for Brighton -- his first in the Premier League -- after being pivotal to Leeds United's promotion from the Championship while on loan in the 2019/20 campaign.
Southgate has opted for a central defender with Manchester United captain Harry Maguire battling to recover from an ankle injury.
Everton defender Ben Godfrey and Southampton captain James Ward-Prowse were other options who both started the Romania game, while Jesse Lingard and Ollie Watkins were also on the standby list, but will now return home.