Under the ordinance, residents cannot drink in a public place or on a public sidewalk or street.
Police spokesman Sgt. Warren Mitchell said the increased enforcement is "specifically for the block party."
"We are not here to kill the mood by writing every citation, because it's not zero tolerance," he said. "I mean, officers will still use their discretion."
Mitchell said police want to curb littering and disorderly conduct in the neighborhoods surrounding Greenville Avenue during the block party and will be more proactive in enforcing the open-container ordinance.
Police have not made changes in how they handle the parade. However, officers will be on the lookout for public intoxication and disorderly conduct, Mitchell said.
The annual parade and block party is the closest thing to a Mardi Gras-like party Dallas has.
"I think this is the one time a year that people can relax and not really worry about that, especially with the ability to walk up and down Greenville with it being blocked off," said Lower Greenville resident Alex Heyed.
She is planning a house party and has already warned her friends about the increased enforcement of the open-container ordinance.
"There's block parties in every other house," Heyed said. "Our plan is to just rope 20 feet out from our sidewalk and let our friends know that, if you walk beyond that, you are taking a risk of getting, I think, it's a $250 fine."
The city expects more than 100,000 people at the events.
Need more information on the St. Patrick's Day parade? Check out this year's Survival Guide.