Alonso jarred his back after bouncing over kerbs during the race in Abu Dhabi nine days ago, with sensors in the Spaniard's Ferrari measuring the impact as he hit the track at 26g.
The 32-year-old underwent precautionary checks at a local hospital after the race and although he was given the all clear, Alonso is known to have been taking anti-inflammatory tablets since.
It had been suggested Alonso would sit out the event at the Circuit of the Americas in Austin, but he is determined to go through the pain barrier as Ferrari battle Mercedes for second place in the constructors' championship.
Via his Twitter account, Alonso said: "Packing the bag for Austin, with some pain, but eager and confident to help the team. I will try to give 100% as always."
It is understood Alonso will undergo checks by FIA medical staff prior to taking to the track ahead of first practice on Friday.
Although not 100 per cent, Ferrari need Alonso to assist them in their championship quest.
The Maranello marque are currently just 11 points behind Mercedes in the standings, with two races remaining, with the difference between second and third worth millions of pounds.
Speaking to the Ferrari website, president Luca Di Montezemolo said: "I am pleased to see Fernando is so keen to give it his all, even when he's not at his best.
"It shows how attached he is to us and I am sure his example will be a further boost for the whole team in its efforts to end this season in the best way possible."