Seven day week probably originated from Babylonian calendar. From there, it spread to the Jews, who were captives under them, and they copied their system of week. It emerged from dividing a synodic lunar month into 3 halves- of 7 days each (and last of 8 days), last of each was considered the day of rest. The discrepancy between the week and month was handled by additional days in the last week- one or two, according to observations. Jews assimilated week into their culture, without these intercalary days. This, then went to Greece, where it was incorporated into the Hellenic astrology, thus assigning the 7 classical planets to each day (actually, to the hours, the presiding planet of hour at the time of the beginning of the day was the presiding planet of the week). When Persian Empire went till the Egypt, this week system was adopted by them. All the abrahamic religions followed the Jews. When Hellenic astrology came to India, it came with the week. The oldest classical Indian astrological texts are Romaka Siddhanta (from Romans), Yavana Jataka (from Greece), Paulisa Siddhanta and others. The Indian Vedanga Jyotish was the original astrological (correctly astronomical) text of India. The twelve zodiacs (Rashis), Seven weekdays, horoscopic astrology, palmistry — all of them are Greek astrology. The Indians had Paksha system (followed till date), and the oldest vedic six day cycle, which we can say week. 6 was chosen, as earlier, the length of year was held to be 366 in some excerpts of Veda, and it was divisible by 6, as well as the sum of 12 synodic cycles- 354. It was handled by adding 2 six day weeks (12 days) at the end of lunar year, known as Dwadasha karma (Ritual of 12 days)- a thing which is observed till date in some of the Rituals. (However, lunar months were separately observed and 2 intercalary months were added in a Yuga (Yuga in vedas and Vedanga Jyotish means 5 year period)). 6 day week fell into disuse very early.
Ramayana, Mahabharata, Vedas, shrauta and early smriti texts never mention Rashis or weekdays.