The National Transport Authority approved the rises in November and they had been due to come in on December 1.
But for 'technical reasons', the Railway Procurement Agency (RPA) said it was not in a position to apply the increases until January 7.
From Monday, an adult return on the Red Line will jump from €4.90 to €5.10, while an adult single on the Red Line has increased from €2.60 to €2.70.
A single adult fare on the Green Line will remain at €2.80, but travelling over both lines through all zones has increased from €2.80 to €2.90
There will be no increases in Child Single, Return or Smart Card/Leap Card fares.
However, some adult Smart Card/Leap Card fares will be raised by between 5c and 10c.
In terms of Smartcard/ Leap card Fares, Adult Red Line has increased from €2.35 to €2.40, Green Line remains at €2.50, travelling over both lines through all zones remains €2.50
A 30-day Student ticket will go from €59.70 to €62.50, but a seven-day fare is staying steady at €18.00
The RPA has defended the rises as "necessary".
"Luas does not receive any operating subvention from the State and in order to maintain this position, it is necessary to increase selected fares at this time," the RPA added.
The price increases come just days after passenger numbers on Luas services set a new record in 2012.
Provisional figures indicate that 29.4m passenger journeys were made last year.
The busiest periods were at the end of August, during the Tall Ships festival, and during the Christmas season.
A Luas extension linking the Red and Green lines is expected to generate an extra 10m passengers in a full year.
Permission was granted last August for a 5.6km extension to the Luas Green Line between St Stephen's Green and Broombridge.
RPA chief executive Rory O'Connor said it was gratifying that Luas continued to operate successfully without any public subvention.
The strong performance last year underpinned Government support for the new extension, he added.
The Luas increases come a day after Dublin Bus increased the price of discounted prepaid tickets, while bus and rail tickets have also gone up.