Aftab,
I'm not sure this helps, but here goes.
From the DR Embassy in Canada website (bold is mine):
"In order to enter the Dominican Republic, citizens of the following countries will require a visa:
Abkhazia, Afghanistan, Algeria, Angola, Armenia, Bahrain, Bangladesh, Belarus, Benin, Bhutan, Bosnia and Herzegovina, Botswana, Brunei, Burkina Faso, Burundi, Cambodia, Cameroon, Cape Verde, Central African Republic, Chad, People's Republic of China, Colombia, Comoros, Congo, Cote d'Ivoire, Cuba, Cyprus, Djibouti, Egypt, Equatorial Guinea, Eritrea, Estonia, Ethiopia, Fiji, Gabon, Gambia, Georgia, Ghana, Guinea, Guinea-Bissau, Haiti, Hong Kong, Jordan, Kazakhstan, Kenya, Kiribati, North Korea, Kosovo, Kuwait, Kyrgyzstan, Laos, Lebanon, Lesotho, Liberia, Libya, Liechtenstein, Madagascar, Malawi, Malaysia, Maldives, Mali, Mauritania, Mauritius, Moldova, Mongolia, Morocco, Mozambique, Myanmar, Nagorno-Karabakh, Namibia, Mauru, Nepal, Nicaragua, Niger, Nigeria, Northern Cyprus, Oman, Pakistan, Palestine, Panama, Philippines, Qatar, Romania, Rwanda, Samoa, Sao Tome and Principe, Saudi Arabia, Senegal, Serbia and Montenegro, Seychelles, Sierra Leone, Singapore, Somalia, Somaliland, South Africa, South Ossetia, Sri Lanka, Sudan, Swaziland, Syria, Tajikistan, Tanzania, Thailand, Timor-Leste, Togo, Tonga, Transistria, Tunisia, Turkey, Turkmenistan, Tuvalu, Ugamda, United Arab Emirates, Uzbekist?n, Vanuatu, Vietnam, Western Sahara, Yemen, Zambia and Zimbabwe."
I'm no immigration specialist but possession of a "Green Card" does not bestow citizenship and on the website they make no distinction for "Green Card" holders, so I suspect that the time distinction cited is the usual time it takes for a "Green Card" holder to acquire US citizenship. I think a Moroccan citizen could hold a "Green Card" for 20 years and if they don't become a US citizen they would still require a Tourist Visa - but I do reserve the right to be wrong.
Good luck.
Gregg