Fellow North London club Tottenham also have been handed a headline tie after being paired against AC Milan, with the first game at the San Siro.
And the interest continues as 2010 Champions Inter Milan face Germany's Bayern Munich in a repeat of last year's final.
Manchester United face French side Marseille, while Chelsea have been draw against Danish outfit FC Copenhagen.
Full 2011 Champions League Second Round Draw===================================
Roma v Shakhtar Donetsk
AC Milan v Tottenham Hotspur
Valencia v Schalke
Inter Milan v Bayern Munich
Lyon v Real Madrid
Arsenal v Barcelona
Marseille v Manchester United
FC Copenhagen v Chelsea