كتاب الحج
15
The Book of Pilgrimage
(72)
Chapter: Validity of a child's hajj, and the reward of the one who takes him for Hajj
(72)
باب صِحَّةِ حَجِّ الصَّبِيِّ وَأَجْرِ مَنْ حَجَّ بِهِ ‏‏
Sahih Muslim 1336 b

Ibn Abbas (Allah be pleased with them) reported:

A woman lifted up her child and said: Messenger of Allah, would the child be credited with having performed the Hajj? Thereupon he said: Yes, and there would be a reward for you.
حَدَّثَنَا أَبُو كُرَيْبٍ، مُحَمَّدُ بْنُ الْعَلاَءِ حَدَّثَنَا أَبُو أُسَامَةَ، عَنْ سُفْيَانَ، عَنْ مُحَمَّدِ بْنِ، عُقْبَةَ عَنْ كُرَيْبٍ، عَنِ ابْنِ عَبَّاسٍ، قَالَ رَفَعَتِ امْرَأَةٌ صَبِيًّا لَهَا فَقَالَتْ يَا رَسُولَ اللَّهِ أَلِهَذَا حَجٌّ قَالَ ‏ "‏ نَعَمْ وَلَكِ أَجْرٌ ‏"‏ ‏.‏
Reference : Sahih Muslim 1336 b
In-book reference : Book 15, Hadith 458
USC-MSA web (English) reference : Book 7, Hadith 3092
  (deprecated numbering scheme)