Canada allows multiple citizenships, so no, the child will not lose Canadian citizenship if he/she also becomes an Indian citizen.
However, based on what I've read on
Indian citizenship, the child will only be granted Indian citizenship if the parent declares that the child does not have a foreign (i.e.: Canadian) passport. And when the child turns 18 years old, he/she will have to decide which citizenship he/she wants to keep, as India does not allow multiple citizenships.
"4. Citizenship by descent.―2 [(1) A person born outside India shall be a citizen of India by descent,―
(a) on or after the 26th day of January, 1950, but before the 10th day of December, 1992, if his father is a citizen of India at the time of his birth;
or (b) on or after the 10th day of December, 1992, if either of his parents is a citizen of India at the time of his birth:
Provided that if the father of a person referred to in clause (a) was a citizen of India by descent only, that person shall not be a citizen of India by virtue of this section unless―
(a) his birth is registered at an Indian consulate within one year of its occurrence or the commencement of this Act, whichever is later, or, with the permission of the Central Government, after the expiry of the said period;
or (b) his father is, at the time of his birth, in service under a Government in India:
Provided further that if either of the parents of a person referred to in clause (b) was a citizen of India by descent only, that person shall not be a citizen of India by virtue of this section, unless―
(a) his birth is registered at an Indian consulate within one year of its occurrence or on or after the 10th day of December, 1992, whichever is later, or, with the permission of the Central Government, after the expiry of the said period;
or (b) either of his parents is, at the time of his birth, in service under a Government in India:
Provided also that on or after the commencement of the Citizenship (Amendment) Act, 2003 (6 of 2004), a person shall not be a citizen of India by virtue of this section, unless his birth is registered at an Indian consulate in such form and in such manner, as may be prescribed,―
(i) within one year of its occurrence or the commencement of the Citizenship (Amendment) Act, 2003(6 of 2004), whichever is later;
or (ii) with the permission of the Central Government, after the expiry of the said period:
Provided also that no such birth shall be registered unless the parents of such person declare, in such form and in such manner as may be prescribed, that the minor does not hold the passport of another country.
(1A) A minor who is a citizen of India by virtue of this section and is also a citizen of any other country shall cease to be a citizen of India if he does not renounce the citizenship or nationality of another country within six months of attaining full age.]
(2) If the Central Government so directs, a birth shall be deemed for the purposes of this section to have been registered with its permission, notwithstanding that its permission was not obtained before the registration.
(3) For the purposes of the proviso to sub-section (1), 1 [any person] born outside undivided India who was, or was deemed to be, a citizen of India at the commencement of the Constitution shall be deemed to be a citizen of India by descent only."
I think you should contact the Indian consulate and ask them about this.