I just downloaded and installed Java for OS X 2014-001 (http://support.apple.com/downloads/DL1572/en_US/JavaForOSX2014-001.dmg). (Double-Click downloaded file /Users/YOURLOGINID/Downloads/JavaForOSX2014-001.dmg; then in resulting Finder window double-click the icon JavaForOSX.pkg; click continue and accept and agree as needed to complete the installation).
Java for OS X 2014-001 includes installation improvements, and supersedes all previous versions of Java for OS X. This package installs the same version of Java 6 included in Java for OS X 2013-005. Please quit any Java applications before installing this update.
Now I am able to run the Minecraft Launcher app.
Only other option (I have not tried this yet) is to download the BETA version of JDK™ 8u20 Early Access Releases: https://jdk8.java.net/download.html JDK™ 8u20 Early Access Releases License Agreement: You must accept the Early Adopter Development License Agreement for Java SE to download this software.
I just downloaded and installed Java for OS X 2014-001 (http://support.apple.com/downloads/DL1572/en_US/JavaForOSX2014-001.dmg).
(Double-Click downloaded file /Users/YOURLOGINID/Downloads/JavaForOSX2014-001.dmg; then in resulting Finder window double-click the icon JavaForOSX.pkg; click continue and accept and agree as needed to complete the installation).
Java for OS X 2014-001 includes installation improvements, and supersedes all previous versions of Java for OS X. This package installs the same version of Java 6 included in Java for OS X 2013-005.
Please quit any Java applications before installing this update.
Now I am able to run the Minecraft Launcher app.
Only other option (I have not tried this yet) is to download the BETA version of JDK™ 8u20 Early Access Releases:
https://jdk8.java.net/download.html
JDK™ 8u20 Early Access Releases
License Agreement:
You must accept the Early Adopter Development License Agreement for Java SE to download this software.