The 23-year-old, who is also taking part in the shot put and discus, finished second behind Martina Hrasnova of Slovakia to pick up 14 points for the host nation towards the team track and field contest.
Skydan told reporters: "I knew from the beginning that the athletes from Slovakia and Moldova were my big rivals. They are as strong as me, but I will not hide.
"I did my best on my last throw to meet my expectations, so I and my team are happy with the results."
The Ukrainian-born athlete, who began representing Azerbaijan earlier this year, finished 18th in the hammer at the London Olympics.