When numbers refer to anything concrete, you need measure words.
English has expressions like "ten head of cattle". When one counts in Chinese, one can say "yī ér sǎn" without measure words, but as soon as numbers refer to anything concrete, you must use measure words.
Some time words are their own measure words: 一分钟 yì fēnzhōng 'a minute', 一天 yì tiān 'one day', 一周 yì zhōu 'one week' and 一年 yì nián 'one year'.
Note however that 一月 yíyuè is January; for 'one month' you have to say: 一个月 yí ge yuè.
With 星期 xīngqī 'week', the most common word for week, again you need ge: 一个星期 yí ge xīngqī 'one week'.
With 礼拜 lǐbài 'week' and 小时 xiǎoshí 'hour', you can either say 一礼拜 yì lǐbài and 一小时 yí xiǎoshí or 一个礼拜 yì ge lǐbài and 一个小时 yí ge xiǎoshí.