The Perth girl had high hopes of taking the gold in the 400m hurdles but was well beaten in the final straight by Jamaica's Kaliese Spencer.
It is the second time Eilidh, has won Commonwealth Games silver in the same event, after achieving the same feat in Delhi four years ago.
She said afterwards: "The first emotion is relief.
"It's been a nervous couple of days and I wanted to execute the race well.
"I felt I did that and I'm delighted to come away with a medal, I'm over the moon.
"I just can't put it into words at the moment. As soon as I crossed the finish line I knew I'd done it.
"I've got a great team around me, and they kept me grounded and focused and I'm happy I could give them something back."
Eilidh finished in of 55.02 seconds, while Spencer won in 54.10.
She was the poster girl of the games, with pictures of her plastered on billboards across the city.
Her appearance at the starting line last night was greeted by deafening cheers amid a sea of Saltires inside Hampden Park.
Jessica Ennis-Hill, the poster girl of London 2012, congratulated Child on Twitter saying: "Congratulation!! Brilliant run! Lots of pressure and pulled it out the bag :) Enjoy celebrating!"
After her second place finish, Eilidh hugged supporters and walked round the track high-fiving and shaking hands with fans.
Her medal took Team Scotland to a total of 43 medals, with three days of competition still to go.
Elsewhere yesterday, Daniel Keatings won gold on the pommel horse and fellow gymnast Daniel Purvis took bronze on the rings.
Alex Gladkov won Scotland's second wrestling bronze.
Louise Martin, Chair of sportscotland, said: "To move on to 43 medals is another fantastic milestone for Team Scotland, and with three more days of competition still to come I can't wait to see how many more we can add.
"Daniel Keatings produced a faultless routine on the pommel horse to take gold, while Eilidh Child performed magnificently at Hampden.
"The bronze medals from Daniel Purvis and Alex Gladkov meant it was four medals for Team Scotland on another successful day."