In the throwback photo, the couple can be seen sitting on a riverside in a hilly area.
The post was well-received by fans, with one user calling them, "you cuties".
Kohli recently stepped down from Team India's T20I captaincy after the T20 World Cup, but still remains ODI and Test skipper. Rohit Sharma has been appointed as the new T20I captain, with Rahul Dravid taking over the head coach role from Ravi Shastri.
The ongoing New Zealand tour of India is Dravid's first assignment as head coach.
In the ongoing first Test match between India and New Zealand, the visitors require 280 runs to win and will have to bat on Day 5.
Initially, India posted a first innings score of 345 with Shreyas Iyer registering a century on his Test debut. In reply, the Blackcaps reached 296. India extended their lead in the second innings, with Iyer bagging a half-century to help his side declare after posting 234 for seven. The visitors ended Day 4 after reaching four for one at Stumps and need 280 runs on Day 5.