Mr Yousafzai, his wife and their two sons flew to the UK last month to be with Malala, who was travelling home from school with two classmates when she was shot at point-blank range.
Mr Yousafzai said: "She wants me to tell everyone how grateful she is and is amazed that men, women and children from across the world are interested in her well-being.
"We deeply feel the heart-touching good wishes of the people across the world of all caste, colour and creed."
Malala, who has been praised for her courage in campaigning for the rights of women and girls in Pakistan, has received thousands of gifts, cards and messages of support.
Among the gifts are pocket money "for sweets", the teenager's favourite CDs, school books, clothing, toys and jewellery, while whole classes of pupils have written letters and messages supporting Malala's campaign for girls' education.
In his statement, issued as new pictures were released showing his daughter sitting up reading a book and looking through cards sent to her, Mr Yousafzai added: "I am awfully thankful to all the peace-loving well-wishers who strongly condemn the assassination attempt on Malala, who pray for her health and support the grand cause of peace, education, freedom of thought and freedom of expression."