Depends on your definition of tactical missile, but no.
Both Malyutka and TOW were brand new back then. They were first employed a year later in Vietnam, and after that in Middle East. India and Pakistan got their respective versions even later. Reasons could be that neither country was that close to, and important for, the two superpowers (India for the Soviet Union, and Pakistan for the USA). Therefore, they only got weapons technology with certain delay.
For example, Pakistan never received the F-4 Phantom II, a plane that Israel, being politically much closer to the USA, already had at that time. They also didn't receive the F-5 which did serve in South Vietnam. Pakistan had the F-86 (already obsolete and replaced in US inventory) and the F-104A, a version that was short-lived in USAAF inventory and replaced by 1971. In fact the US arms embargo, introduced after the India-Pakistan war of 1965, was still in effect a few years after the 1971 war.
The Soviet Union was more pragmatic in this regard, so they did supply India with certain weapon types cleared for export. India had the Mig-21 FL, a somewhat downgraded version for Third World countries. They also received P-15 Termit and T-54/55 tanks, but S-75 Dvina was never sold to India. Usual Soviet policy at that time was to sell relatively modern equipment to Third World allies, but somewhat downgraded and already introduced into Soviet service. This is opposite of modern Russian practice to sometimes sell newest and not yet introduced equipment to countries like India, in order to gain necessary funds.
One thing worth mentioning is that neither side had ballistic missiles at that time. At that time US did not develop short ranged ballistic missiles, and did not sell them to allied countries. PGM-11 Redstone was already retired in 1971. Soviet Union did offer Scud and Luna missiles on the international market, but again first and foremost to closer allies and in any case after 1971. Both India and Pakistan later developed nuclear weapons and their own indigenous ballistic missiles for delivery.
As a final note, it appears that both sides did not posses multiple rocket launchers in their artillery units during the war. This is somewhat strange, especially since Soviet Union did export BM-13, BM-14 and BM-21 in those years. Instead, both India and Pakistan appear to have relied on conventional tube artillery.