Azpilicueta was caught in the face by the boot of Southampton striker Sekou Mara as the Frenchman attempted an overhead kick.
The Chelsea captain appeared to lay motionless on the pitch for several minutes before he was taken off on a stretcher in a conscious state.
Azpilicueta spent the night in hospital but has now given a positive feedback regarding his situation.
"Hi everyone! Thank you all for your love and messages of support! My family and I would like to thank everyone who has been looking after me since yesterday's incident," the defender tweeted, along with a photo of him smiling and giving a thumbs-up.
"From the Chelsea medical team, to team-mates and opponents, to St Mary's and Cleveland Hospital and all staff members and doctors: a massive thank you from the bottom of my heart.
"Now, time to recover and I will see you soon on the pitch!"
Chelsea lost 1-0 to Southampton at Stamford Bridge on Saturday, leaving them in 10th position.
Azpilicueta has made 26 appearances for Chelsea this season.
