The Argentina forward – who made his Paris Saint-Germain debut last week – was the victim of a shin-high challenge from his opponent, and crumpled to the ground.
Replays showed that his leg – which bared all the weight – bent backwards as a result of the tackle.
Messi remained down for a few minutes and received treatment, but thankfully did not suffer serious injury.
Martinez was originally booked by the referee for the shocking challenge, with VAR later upgrading it to a red card.
The incident occurred midway through the first half, with both teams level at 0-0.
Argentina took the lead in first half stoppage time, with Lautaro Martinez beating through the offside trap and slotting into the bottom corner.
They made it 2-0 after the break when Martinez laid the ball off for Joaquin Correa to take a touch and fire the ball into the back of the net.
Angel Correa then put the finishing touches on an excellent team move, which featured a number of one-touch passes in and around the area and resulted in an initial save from the goalkeeper.
Venezuela scored what ended up being a consolation goal deep in stoppage time, with Yeferson Soteldo notching from the penalty spot on 94 minutes.
Argentina remain second in South American qualifying for the World Cup, six points behind leaders Brazil – who they face on Sunday.
The Copa America champions have won four and drawn three of their seven qualifiers so far. They defeated Ecuador, Bolivia and Peru, as well as recording draws against Paraguay, Chile and Colombia.
Featured Image Credit: Getty